Recently, Bennett et al. [Eur. J. Phys. 37:014001, 2016] presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, $\hat H$, and the electric and magnetic field observables, $\hat {\bf E}$ and $\hat {\bf B}$, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect.

The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light remains always the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterward, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

This short paper briefly explores the interplay between quantum mechanics and gravity, drawing from the principle of gravitational redshift and bringing it into quantum mechanical frameworks. The exploration looks through quantum mechanical relations and equations such as Planck-Einstein relation, De-Broglie’s relation and the relativistic wave equations, and propagators, accounting for the presence of gravitational fields through gravitational redshift of its momentum.

This paper investigates the problem of a relativistic Dirac half-integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. In total, the tunneling time always remains positive for particle states while it becomes negative for antiparticle ones. Furthermore, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study’s results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.

Relativistic atomic and molecular structure calculations start from very different premises to quantum electrodynamics (QED). QED predicts radiative corrections that can nly be approximated crudely in today's atomic structure programs. This paper describes rigorous simple algorithms for including accurate vacuum polarization and self-energy corrections in the GRASP programs.

An evanescent wave is a non-propagating wave with an imaginary wave vector. In this study, we prove that these are solutions of the tachyon-like Klein–Gordon equation, and that in the tunneling of ultrarelativistic spin-1/2 particles they describe superluminal states arising from interactions between a particle and barrier. These states decay as a particle emerges from the opposite side of a potential barrier, conserving the same initial energy but not necessarily the same mass. The obtained theory is applied to the neutrino, to explain flavor oscillations during free flight and determine the conditions that maximize the probability of their occurrence.

An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation keeping the form of the particle fixed but decaying its amplitude. An analogy with Maxwellian equations is presented. Massive electromagnetic field will satisfy a quantum Telegraph equation instead of a pure wave equation. This equation resembles the motion of the electromagnetic field in a conducting medium. With a particular setting of the scalar and vector wavefunctions, the dual quantum equations are found to yield the quantized Maxwell's equations. The total energy of the particle is related to the phase velocity ($v_p$) of the wave representing it by $E=p\,|v_p|$, where $p$ is the matter wave momentum. A particular solution which describes the process under which the particle undergoes a creation and annihilation is derived. The force acting on the moving particle is expressed in a dual Lorentz-like form. If the particle moves like a fluid, a dissipative (drag) quantum force will arise.

An exhaustive list of thirteen instances of reports confirming experimentally the relativistic Doppler relation, are examined. For those involving longitudinal Doppler, the non-relativistic relation is seen to be confirmed, within the reported experimental accuracies, to the same degree as the standard relativistic relation. Higher values of the speed of the emitter would be required to examine further the claimed confirmations. For those reports involving saturation spectroscopy, there is much confusion over the appropriate Doppler relation to be used, together with some serious analytical flaws. For the two cases that involve transverse Doppler, there are seen to be either serious faults in the theoretical part, or intrusion from the first order effect. Therefore, the reported conclusions - that the results for the experiments confirm the relativistic SR relation - cannot be justified by any of the experimental works.

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

We study the center of energy (CE) before and after the separation of superposed wave from a moving medium (MM). It is assumed that two out-of-phase mechanical transverse waves propagating from the opposite directions on a medium moving at non-relativistic speeds are superposed and the superposed portion (SP) is separated from the MM at that moment. We consider the CE of the SP before and after the separation from the MM. The location of CE (LCE) of the SP seems to be at the center of it at the moment of superposition. The SP rotates due to the separation from the MM since the velocity of each portion symmetric with respect to the center of the SP is equal in magnitude and opposite in direction. The magnitudes of velocities of the symmetric portions become different as soon as the SP begins to rotate with the separation from the MM. Then the energies of their symmetric portions are not the same, so the LCE of the SP is not at the center of it. As a result, the LCE of it looks different before and after the separation from the MM. We must find a solution to keep the LCE of the SP constant. We propose that two out-of-phase mechanical transverse waves (MTWs) propagating from the opposite directions on a MM originally have hidden difference in relativistic energy and it suddenly appears within the range observable in Newtonian mechanics when the SP starts rotating. This means that the point of view of hidden difference in relativistic energy is necessary to keep the LCE constant.

With simple but rigorous arguments we prove that the ordinary second quantization of bosonic and fermionc fields is formally equivalent to constraining the elementary degrees of freedom of the classical fields to have intrinsically periodic dynamics in time. This result confirms and extends the formal equivalence obtained in previous papers for general Hamiltonian systems in terms of canonical quantization, for elementary relativistic particles also in terms of the Feynman Path Integrals, as well as other remarkable correspondences of both phenomenological and theoretical fundamental interest.

The meaning and evolution of the notion of “temperature” (which is a key concept for the condensed and gaseous matter theories) is addressed from the different points of view. The concept of temperature turns out to be much more fundamental than it is conventionally thought. In particular, the temperature may be introduced for the systems built of “small” number of particles and particles in rest. The Kelvin temperature scale may be introduced into the quantum and relativistic physics due to the fact, that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of the temperature to the metrics of the configurational space describing the behavior of system built from non-interacting particles is demonstrated. The Landauer principle asserts that the temperature of the system is the only physical value defining the energy cost of isothermal erasing of the single bit of information. The role of the temperature the cosmic microwave background in the modern cosmology is discussed.

The transport and entanglement of photons is becoming prominent in optics applied to information and quantum computing, where the angular momentum of light stands out in the exchange and inversion of quantized states, with prospects for several technological applications, such as the transport and storage of quantum information. In order to contribute to the understanding of quantized states in photon-matter interaction, we describe a quantized state equation in multidimensional Hilbert space for the diagnosis of OAM states, where probabilities arise in a relativistic setting. It was found that the classical-relativistic variability of the probabilities constitutes a resultant capable of describing the quantized states of light, where the state variable is the variation of the angular momentum of the photon, capable of estimating the orbital angular momentum inversion points at angular incidence. It was found that the chances of finding the quantized states of light at angular incidence can be treated by purely relativistic probabilities, explaining that when both states have equal chances of being found and the angular momentum variation is zero, the source-observer synchronizations occur at the step of increasing relativistic regime of the photon dynamics. We found that the relativistic effect from the perspective of the source referential is able to alter the chances of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.

The quasi-two-dimensional organic charge-transfer salt κ-(BEDT-TTF)₂Cu₂(CN)₃ is one of the prime candidates for a quantum spin-liquid due the strong spin frustration of its anisotropic triangular lattice in combination with its proximity to the Mott transition. Despite intensive investigations of the material's low-temperature properties, several important questions remain to be answered. Particularly puzzling are the 6 K anomaly and the enigmatic effects observed in magnetic fields. Here we report on low-temperature measurements of lattice effects which were shown to be particularly strongly pronounced in this material (R. S. Manna et al., Phys. Rev. Lett. 104, 016403 (2010)). A special focus of our study lies on sample-to-sample variations of these effects and their implications on the interpretation of experimental data. By investigating overall nine single crystals from two different batches, we can state that there are considerable differences in the size of the second-order phase transition anomaly around 6 K, varying within a factor of 3. In addition, we find field-induced anomalies giving rise to pronounced features in the sample length for two out of these nine crystals for temperatures T < 9 K. We tentatively assign the latter effects to B-induced magnetic clusters suspected to nucleate around crystal imperfections. These B-induced effects are absent for the crystals where the 6 K anomaly is most strongly pronounced. The large lattice effects observed at 6 K are consistent with proposed pairing instabilities of fermionic excitations breaking the lattice symmetry. The strong sample-to-sample variation in the size of the phase transition anomaly suggests that the conversion of the fermions to bosons at the instability is only partial and to some extent influenced by not yet identified sample-specific parameters.

If "quantization is an art" then it can be greatly rened by adopting cyclic time formalism. In past papers we have proven the effectiveness of a formulation of physics based on cyclic relativistic time. Now we can demonstrate in a general way, by using theorems of Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics directly imply the ordinary canonical commutation relations and the other Dirac's rules of canonical Quantum Mechanics. In other words, according to our result, canonical quantization is an implicit way of imposing intrinsically cyclic time dynamics without explicitly saying that time is a cyclic dimension.

We show that the quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems allowing exposing its falsity.

From the theory of relativistic chemical kinetics [M. W. Baig, Int. J. Mod. Phys. B 31, 1750177 (2017)] relativistic thermodynamics and kinetics for electrode processes have been developed to explain time dilation for electrode processes. For a moving observer moving at fractions of the speed of light, cell potential is observed to decrease. This results in the slower oxidation and reduction of ions at the respective electrodes. The newly formulated Lorentz transformation of the electrode and cell potential is explained in terms of generation of spin 2-boson “gravitons” from fusion of spin-1 boson “virtual-photons” mediating electrostatic force of attraction between ions and electrodes. It is postulated that birth of spin 2-boson i.e. gravitons is followed by their eventual escape in any of higher 4+n dimensions. To demonstrate the effectiveness of the present theory, the Daniel cell is considered as a numerical example.

Analytical modeling has symmetries and aesthetic-mathematical characteristics that distinguish it from numerical computation. Nanoscience plays an extremely important role in unification efforts that also include holistic aspects of reality. In this paper I present new discovered results about the complete analytical quantum relativistic form of the mean square deviation of position false related to a lately appeared Drude-Lorentz-like model (DS model), already performed at classical, quantum and relativistic level. The function false gives precise information about the distance crossed by carriers (electrons, ions, etc.) inside a nanostructure, considering both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but it holds from sub-pico-level to macro-level because of the existence of a gauge factor, making it applicable to every oscillating processes in Nature. Examples of application and suggestions supplement the paper, as well as interesting developments to be studied related to the model and to one of the basic elements of a current unified holistic approach based on the vacuum energy.

This paper attempts to describe the large-scale (solar system-like, astronomical-scale) systems of the known world using the physical models and mathematical tools of relativistic quantum mechanics. The value of H_x can be introduced and approximated as an analogue of the constant ℏ. Based on the quantum mechanical approach, the proper time scale of the solar system can be determined.

Superscaling in electron scattering from nuclei is re-examined paying special attention to the definition of the averaged single-nucleon responses. The validity of the extrapolation of nucleon responses in the Fermi gas has been examined, which previously lacked a theoretical foundation. To address this issue, we introduce new averaged responses with a momentum distribution smeared around the Fermi surface, allowing for momenta above the Fermi momentum. This approach solves the problem of negativity in the extrapolation away from the scaling region and, at the same time, validates its use in the scaling analysis. This work has important implications for the interpretation of scaling data and contributes to the development of a more complete understanding of the scaling approach.

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multi-fluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein-Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called ``$3 + 1$'' form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed ``flow-of-time''. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the ``$3 + 1$'' form of the field equations which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe.

Novel approaches under the extreme conditions of ultra-high gravity of a super massive black hole allow us to assume that the spacetime degrades into the single dimension of time. A unique interpretation of the non-relativistic Schrödinger equation together with the relativistic Klein-Gordon and Dirac equations is presented by swapping the three dimensional space derivatives with the singular time derivative in the D’Alembertian operator. This apparatus reveals a unique time dependent wave equation that results in some implications such as possible time quantization with the intervals of around 3.36 × 10−21 ? which is in the order of uncertainty in time, ∆? = 1.3 × 10−21 ?, calculated from the energy-time version of the Heisenberg uncertainty principle for electrons. As a result of this, an antisymmetric wave function around the edge of the event-horizon zone appears and indicates that the virtual particle-antiparticle pairs of the electron field split into two real components with the spin-up and down states, reconfirming the Hawking radiation. Energy eigenvalues calculated from the application of the Dirac equation satisfies the preservation of energy and charge. The wave equation invoked in this study reduces into the time dependent Dirac equation within the neighborhood of zero-point, ? = 0, insuring the relevance of the evaluations.

One of the biggest challenges in modern physics is how to unify gravity with quantum theory. There is an absence of a complete quantum theory of gravity, and conventionally it is thought that the effects of quantum gravity occur only at high energies (Planck scale). Here we suggest that certain novel quantum effects of gravity can become significant even at lower energies and could be tested at laboratory scales. We also suggest a few indirect effects of dark energy that can show up at laboratory scales. Using these ideas, we set observational constraints on radio recombination lines of the Rydberg atoms. We further suggest that high-precision measurements of Casimir effects for smaller plate separation could also show some manifestations of the presence of dark energy.

The paper proposes a theoretical study that investigates the quantum effects on the gravity of black holes. The study utilizes a gravitational model that incorporates quantum mechanics derived from the classical-like quantum hydrodynamic representation. The research calculates the mass density distribution of quantum black holes, specifically in the case of central symmetry. The gravity of the quantum black hole shows contributions coming from the quantum potential energy, which is also sensitive to the presence of the background of gravitational noise. The additional energy, stored in the quantum potential fluctuations and constituting a form of dark energy, leads to a repulsive gravity in the weak gravity limit. This repulsive gravity overcomes the attractive classical Newtonian force at large distances of order of the intergalactic length.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

Time, traditionally viewed as a linear, non-dynamic parameter, is re-envisioned in this study as a Hyperdimensional concept. This paper conducts a cross-disciplinary examination, critically analysing the conceptualization of time in classical mechanics, quantum mechanics, and cosmology to propose a ground breaking reconceptualisation that extends beyond conventional frameworks. In classical mechanics, time is perceived as an absolute, continuously progressing backdrop, largely independent of events. Quantum mechanics treats time as a static parameter that does not influence quantum states but provides a framework for their evolution. In cosmology, time is considered a dimension that emerges from the Big Bang and serves as a measure for the universe's expansion, yet it does not interact with the structural dynamics of the cosmos. Challenging the transformative insights of Einstein’s relativity, which merges time with spatial dimensions under extreme conditions, we advocate for a perspective that views time as a Hyperdimensional and universal constant. This perspective posits that time, despite its unique and intrinsic properties, does not dynamically interact with or alter physical phenomena. Instead, it underpins our understanding of phenomena across different scales—from the minutiae of quantum states to the macroscopic dynamics of cosmology—without direct causation or change. A critical examination of time dilation and relativistic assumptions reveals significant discrepancies in traditional interpretations, particularly in how they are applied across different physical contexts. Our findings challenge the uniform applicability of time dilation, suggesting that observed phenomena often attributed to relativistic effects might better be explained through non-relativistic mechanisms such as phase shifts or changes in wavelength rather than temporal dilation. By synthesizing insights from various scientific domains, we advocate for a unified theory that recognizes time as a fundamental, universal dimension that is conceptual and non-interactive. Our goal is to bridge existing gaps between diverse scientific interpretations and promote a more integrated, profound understanding of time's autonomous and intrinsic nature.

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e. with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e. the concept of neutron's (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle's dynamics from the quantum dynamics of the scatterer---a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, 'which-path detection' versus interference, von Neumann measurement, Week Values, etc.) new observable effects may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. 7

A semi–numerical approach proposed many years ago for describing gravitational collapse in the post–quasi–static approximation , , , , is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi–homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post–quasi–static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids and therefore we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g. luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

We consider subtleties of the horizon (null-hypersurface) limit in the Parikh-Wilczek Membrane Approach to Black Holes. Specifically, we refine the correspondence between the (projected) Einstein equations of gravity with matter and the Raychaudhuri-Damour-Navier-Stokes (RDNS) equations of relativistic hydrodynamics. For a general configuration of gravity with matter we obtain additional terms in the hydrodynamic equations, which include logarithmic derivarives of a parameter (the regularization function) determining the proximity of a stretched membrane to the BH horizon. Direct computation of the new terms for exact (Schwarzschild and Kerr) solutions to the Einstein equations results in vanishing the additions to the RDNS equations in the horizon limit. For spacetimes, which are not exact solutions to the Einstein equations, as, for instance, for space-time configurations mimicking black holes, taking into account new terms in the RDNS equations is the mandatory operation. We also comment the correspondence between the horizon limit of the Parikh-Wilczek Membrane Approach and the Gourgoulhon-Jaramillo method of a null-hypersurface description, as well as the link of the obtained results to our previous work on the Kerr black holes.

The G2 gas cloud motion data and the scarcity of observations on the event horizon-scale distances have challenged the comprehensiveness of the central supermassive black hole model. In addition, the Planck Legacy 2018 release has preferred a positively curved early Universe with a confidence level higher than 99%. This study investigates the impact of the background curvature and its evolution over the conformal time on the formation and morphological evolution of central compact objects and the consequent effect on their host galaxies. The formation of a galaxy from the collapse of a supermassive gas cloud in the early Universe is modeled based on interaction field equations as a 4D relativistic cloud-world that flows and spins through a 4D conformal bulk of a primordial positive curvature considering the preference of the Planck release. Owing to the curved background, this scenario of galaxy formation reveals that the core of the galaxy undergoes a forced vortex formation with a central event horizon leading to opposite vortices (traversable wormholes) that spatially shrink while evolving in the conformal time. It indicates that the galaxy and its core are formed in the same process whereas the surrounding gas clouds form the spiral arms due to the frame-dragging induced by the fast-rotating core. It demonstrates that the accretion flow onto the central supermassive compact object only occurs at the central event horizon of the two opposite vortices while their other ends eject the relativistic jets. This can elucidate the relativistic jet formation and explain the G2 gas cloud motion if its orbit is around one of the vortices but at a distance from the central event horizon. The gravitational potential of the early curved bulk could contribute to galaxy formation while the present spatial flatness deprives the potential of bulk which could lead to galaxy quenching. The formation of a galaxy and its core simultaneously could explain the growth of the supermassive compact galaxy core to a mass of ~10⁹ M_⊙ at just 6% of the current Universe age.

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydrodynamics, on top of a known class of solutions describing Hubble-expansion. We describe the properties of this class of perturbative solutions, and investigate a few selected solutions in detail.

An analysis of the consistency of the Abraham and Minkowski momenta in the determination of the photon trajectory was carried out considering a new principle of conservation of the photon's mechanical energy, in which the photon conserves translational energy in orbital angular momentum when transiting between two media, introducing the relativistic energy wave (REW). The confrontation between REW and the recent theory of space-time waves (ST) was considered, pondering your differences. Throughout this study it was possible to verify that the Abraham momentum appears a relativistic photon ignition device in the transition between two media, acting as the hidden momentum of the Minkowski’s relativistic momentum. The wavy behavior in the matter is relativistic, and the relativistic trajectory appears with delays and advances, with points of synchronization between source-observer. The classical or relativistic trajectories are determined as a function of the angle of incidence and the relative refractive index, by one of two distinct non-additive torques, the classic by Abraham or the relativistic by Minkowski. It was found that the same analysis conducted under the principle of conservation of the mechanical energy of the photon can be treated by an new Doppler, Relativistic Apparent, that can be confused with other Dopplers in the treatment of redshift from distant sources. It was found that the conservation of energy in Orbital Angular Momentum (OAM), in the interaction with matter, explains that the synchronization instants are found in the inversion of the OAM, where the advances and delays of REW occur under negligible variations of the OAM, however, opposites.

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

We explore an idea put forward many years ago by Zeldovich and Novikov concerning the existence of compact objects endowed with arbitrarily small mass. The energy-density of such objects, which we call “Ghost stars”, is negative in some regions of the fluid distribution, producing a vanishing total mass. Thus, the interior is matched on the boundary surface to Minkowski space-time. Some exact analytical solutions are exhibited and their properties are analyzed. Observational data that could confirm or dismiss the existence of this kind of stellar object, is commented.

Current spacecraft mass are mostly fuel, this is dictated by the lack of fueling stations in space and also by the Tsiolkovsky rocket equation which defines the mass ratio needed to escape earths gravity. The Tsiolkovsky rocket equation gives a relationship between the mass ratio and the final velocity in multiples of the exhaust speed, and dictates a high mass ration for current exhaust speeds. A relativistic motor exchanging momentum and energy with the electromagnetic field may mitigate such considerations, enabling efficient interplanetary travel. In this paper we will discuss the advantages and challenges of this novel mover for space transportation.

In this review article the study of the development of relativistic cosmology and introduction of inflation in it is carried out. We study the properties of standard cosmological model developed in the framework of relativistic cosmology and the geometric structure of spacetime connected coherently with it. We examine the geometric properties of space and spacetime ingrained into the standard model of cosmology. The big bang model of the beginning of the universe is based on the standard model which succumbed to failure in explaining the flatness and the large-scale homogeneity of the universe as demonstrated by observational evidence. These cosmological problems were resolved by introducing a brief acceleratedly expanding phase in the very early universe known as inflation. Cosmic inflation by setting the initial conditions of the standard big bang model resolves these problems of the theory. We discuss how the inflationary paradigm solves these problems by proposing the fast expansion period in the early universe.

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting form the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

In this study, we investigated, for the first time, the effects of the spatially varying effective mass, asymmetry parameter, and well width on the electronic and optical properties of the quantum well which has an improved Rosen-Morse potential. Calculations are made within the framework of the effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal functions to find eigenvalues and eigenfunctions of the electron confined within the improved Rosen-Morse potential. Our results show that the position-dependence mass, asymmetry, and confinement parameters cause significant changes in the electronic and optical properties of the structure we focus on since these effects create a significant increase in electron energies and a blue shift in the absorption spectrum. The increase in energy levels enables the development of optoelectronic devices that can operate at wider wavelengths and absorb higher energy photons. This offers potential advancements in fields such as optical communication, imaging technology, and solar cells.

Intraband energy transitions of an electron in GaAs/AlGaAs hexagonal quantum well wires in the presence of external electric and magnetic fields are presented. We consider the effects of the revolve of the quantum well wires via a geometric factor that converts the quantum wires straight and symmetric with respect to the z−axis, into a curved wires that no longer has this symmetry. In addition, the influence of having a shallow donor impurity on (off) is calculated. The shape of this quantum string corresponds to the core/shell structure. The energy levels and wave functions of the electron in the heterostructure with a finite potential between the shells are calculated using the effective mass approximation and the finite element method. The calculations of the optical properties are obtained from the compact density matrix and an iterative method. The direction of the applied external fields is parallel (anti-parallel) to the z−direction. The results reveal a significant dependence of the physical properties calculated with the deformation parameter, the dimensions of the quantum well wires and the presence or not of the impurity. The electronic transitions are in a range between 4.90 meV to 41.50 meV under the effect of the electric field, this corresponds to a range of frequencies of optical responses between 1.20 to 10 THz, that is, the mid-infrared. For the magnetic field the range is between 1.24 meV to 14 meV, that is, in frequencies from 0.36 to 3.38 THz, that is, in the far-infrared.

The phenomenal mathematical efficiency of quantum field theories in modern high-speed information and communication systems has a very simple explanation from the point of view of common sense and higher mathematical logic: all of them – quantum cosmology, quantum physics, quantum metrics and quantum calculus – are the self-informational mathematical systems based on symbolic and numerical functional analysis and elementary recursive calculations of interrelated space and time parameters of matter motion in various states of the material environment.For the first time in scientific and engineering practice, it was clearly shown that the information entropy of both standard symbolic and non-standard numerical functional analysis has absolute exact limits of computational accuracy – 1/10^16 and 1/10^64, respectively. Moreover, the second limit determines the maximum level of accuracy of practical quantum metrics and calculations and fully coordinates four branches of classical physics – thermodynamics, electrodynamics, gravidynamics, chromodynamics with special and general relativity.

Understanding the stability limit of crystalline materials under variable tensile stress conditions is of capital interest for their technological applications. In this study, we present results from first-principles density functional theory calculations that quantitatively account for the response of selected covalent and layered materials to general stress conditions. In particular, we have evaluated the ideal strength along the main crystallographic directions of 3C and 2H polytypes of SiC, hexagonal ABA stacking of graphite and 2H-MoS2. Transverse superimposed stress on the tensile stress was taken into account in order to evaluate how the critical strength is affected by these multi-load conditions. In general, increasing transverse stress from negative to positive values leads to the expected decreasing of the critical strength. Few exceptions found in the compressive stress region correlate with the trends in the density of bonds along the directions with the unexpected behavior. In addition, we propose a modified spinodal equation of state able to accurately describe the calculated stress-strain curves. This analytical function is of general use and can also be applied to experimental data anticipating critical strengths and strains values and providing informattion on the energy stored in tensile stress processes.

Herein is introduced a simple scalar field model derived from classical based kinetic energy, gravitational potential energy, and Special Relativity’s rest mass energy. By applying a classical orbit over the scalar field, relativistic effects are predicted. The scalar field is then applied to a classical model of the Hydrogen atom resulting in a relativistic effect equal to the binding energy of the Hydrogen atom. In addition, the model derives the fine structure constant due to the gravitational effect. The relativistic effects are then discretized in increments equal to the model’s gravitational induced constant. The discretization produces the Hydrogen atom spectral emissions and an angular moment equal to Planck’s reduced constant. The model is not presented as a replacement for current theory, rather it is for inspection and illustration of how a simplistic model may offer a fundamental bridge between the more complex, time proven theories of General Relativity and Quantum Mechanics.

The shortage of quantum computers, and their current state of development, constraints research in many fields that could benefit from quantum computing. Although the work of a quantum computer can be simulated with classical computing, personal computers take so long to run quantum experiments that they are not very useful for the progress of research. This manuscript presents an open quantum computing simulation platform that enables quantum computing researchers to have access to high performance simulations. This platform, called QUTE, relies on a supercomputer powerful enough to simulate general purpose quantum circuits of up to 38 qubits, and even more under particular simulations. This manuscript describes in-depth the characteristics of the QUTE platform and the results achieved in certain classical experiments in this field, which would give readers an accurate idea of the system capabilities.

External quantum efficiency of industrial-grade green InGaN light-emitting diodes (LEDs) has been measured in a wide range of operating currents at various temperatures from 13 K to 300 K. Unlike blue LEDs, the efficiency as a function of current is found to have a multi-peak character, which could not be fitted by a simple ABC-model. This observation correlated with splitting of LED emission spectra into two peaks at certain currents. The characterization data are interpreted in terms of non-uniformity of the LED active region, which is tentatively attributed to extended defects like V-pits. We suggest a new approach to evaluation of temperature-dependent light extraction and internal quantum efficiencies taking into account the active region non-uniformity. As a result, the temperature dependence of light extraction and internal quantum efficiencies have been evaluated in the temperature range mentioned above and compared with those of blue LEDs.

Quantum correlations, especially time correlations, are crucial in ghost imaging in order to significantly reduce the background noise on the one hand while increasing the imaging resolution. Moreover, the time correlations serve as a critical reference, distinguishing between signal and noise, which in turn enable clear visualization of biological samples. Quantum imaging also addresses the challenge involved in imaging delicate biological structures with minimal photon exposure and sample damage. Here we explore the recent progress in quantum correlation-based imaging, notably its impact on secure imaging and remote sensing protocols as well as on biological imaging. We also exploit the quantum characteristics of heralded single-photon sources (HSPS) combined with decoy-state methods for secure imaging. This method uses Quantum Key Distribution (QKD) principles to reduce measurement uncertainties and protect data integrity. It is highly effective in low-photon-number regimes for producing high-quality, noise-reduced images. The versatility of decoy-state methods with WCSs (WCS) is also discussed, highlighting their suitability for scenarios requiring higher photon numbers. We emphasize the dual advantages of these techniques: improving image quality through noise reduction and enhancing data security with quantum encryption, suggesting significant potential for quantum imaging in various applications, from delicate biological imaging to secure quantum communication.

We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

In this paper, we solve KG-oscillator in the five-dimensional cosmic string space-time background with a uniform magnetic field and quantum flux subject to a scalar potential of Cornell-type using KaluzaKlein theory, and observe the gravitational analogue of the AharonovBohm effect. We show that the energy eigenvalue and eigenfunction depends on the global parameters of the space-time, and also a quantum effect is seen due to the dependence of magnetic field on the quantum numbers of the system

We review some properties of a relativistic classical massless charged particle with spin interacting with an external electromagnetic field. We give in particular a proper definition of kinetic energy and total energy, the latter being conserved when the external field is stationary. We find that the particle’s velocity may differ from c as a result of the spin - electromagnetic field interaction, without jeopardizing Lorentz invariance.

This Article demonstrates how an eigendecomposition problem is inputted into a quantum circuit, how gates are applied in the quantum circuit, and how the output measurements are the correct eigenvalues. This process is known as quantum phase estimation (QPE). A quantum harmonic oscillator example, a foundational quantum physical chemistry problem, is demonstrated within the context of QPE. A particle in a box example, another quantum physical chemistry problem, may be solved by QPE with a caveat. These examples are of the limiting cases of diagonal matrices. Future advances in taking matrix inverses for solving linear sets of equations or finding ground state energies in the Schrödinger equation will use the principles implemented in this Article.

We develop a renormalizable model of Quantum General Relativity (QGR). We do this by building on earlier work with quantum electrodynamics (QED). Working with the Feynman path integral (FPI) approach to QED, we generalize the paths from varying in space to varying in space and time. This gives the standard results plus dispersion in time of order attoseconds or left. Over longer times, the dispersion in time averages out, but at attosecond times it should be detectable with current technology. As an unexpected but welcome side-effect, the approach caused the usual loop integrals to be finite. Since the usual UV divergences are significantly harder to renormalize in QGR than in QED, and since using paths in time plus space is definitely more in keeping with the general spirit of GR, we here apply the same approach to QGR. We show that with an appropriate choice of gauge (trace-reversed de Donder gauge) we can extend the earlier results to include QGR. Sub-attosecond measurements of individual gravitons are not within our reach, but at least the ultraviolet divergences in QGR are contained in the same way. We have therefore a renormalizable model of QGR

1) We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time $t$. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time $t_0$ under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove that both these situations cannot arise under ordinary circumstances and thus measurement processes cannot be modelled by physical Hamiltonians.

We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a way that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly in performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT's internal quantum network

Starting with a particle in the cube system, we investigate the exotic possibility that the quantum numbers (n_x,n_y,n_z) satisfy the Markov equation. We find that the proposed particle in the Markov-cube system follows from a non-classical information entropic space by the quantum potential Q. We study the classical correspondents of the proposed particle in the Markov-cube system. According to our proposition, this particle identified by detailed measurements of the confinement particle-energy levels is an artifact or occurs in nature.

Light is an electromagnetic radiation that has visible and invisible wavelength spectrum. The visible light can only be detected by the eyes through the optic pathways. With the presence of scalp, cranium and meninges, the brain is seen as being protected from direct exposure to light. For that reason, the brain can be viewed as a black body lying inside a black box. In physics, a black body tends to be in thermal equilibrium with its environment and can tightly regulate its temperature via thermodynamics principles. Therefore, a healthy brain inside a black box should not get exposed to light. On the contrary, photobiomodulation, a form of light therapy to the brain has been shown to have beneficial effects for some neurological conditions. The proposed underlying mechanisms are multiple. Herein we present our intraoperative findings of rapid electrocorticographic brainwave changes when the brain was shone directly with different wavelengths of light during awake brain surgery. Our findings provide literature proof on light’s ability to influence human brain energy and function. Our proposed mechanism for these rapid changes is the presence of plasma-like energy inside the brain which causes fast brain activities that are akin to lightning strikes.

Engineering of quantum computers requires reliable characterization of qubits, quantum operations, and even the entire hardware. Quantum tomography is an indispensable framework in quantum characterization, verification, and validation (QCVV), which has been widely accepted by researchers. According to the tomographic target, quantum tomography can be categorized into quantum state tomography (QST), quantum process tomography (QPT), gate set tomography (GST), process tensor tomography (PTT), and instrument set tomography (IST). Standard quantum tomography toolkits generally consist of basic linear inverse methods and statistical maximum likelihood estimation (MLE) based methods. Furthermore, the performance of standard methods, including effectiveness and efficiency, has been further developed by exploiting Bayesian estimation, neural networks, matrix completion techniques, etc. In this review, we introduce the fundamental quantum tomography techniques, including QST, QPT, GST, PTT, and IST. We first introduce the details of basic linear inverse methods. Then, the framework of MLE methods with constraints is summarized. Finally, we briefly introduce recent further research in developing the performance of tomography. This review provides a primary getting-start in developing quantum tomography, which promotes quantum computer development.

Models of quantum measurements are presented, including observers subject to the laws of quantum mechanics. Observers perform multiple measurements in an attempt to disprove the collapse hypothesis. It is shown that under reasonable assumptions the effort cannot succeed. Under a unitary evolution the end state is a correlation between the result of the first measurement and the result(s) of the others, consistent with the observer's collapse hypothesis. The observer may conclude that the laws of nature include a non-unitary collapse mechanism, even if one does not actually exist. Discard of information is the crucial factor which distinguishes entanglement from measurement.

Using the projection evolution (PEv) approach, time can be included in the quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper we discuss the possibility of constructing a quantum clock, which advances in time during its quantum evolution, in each step having some probability to localize itself on the time axis in the new position. We propose a working two-state model as the simplest example of such a clock.

True randomness is necessary for the security of any cryptographic protocol, including quantum key distribution (QKD). In QKD transceivers, randomness is supplied by one or more local private entropy sources of quantum origin, which can be either passive (e.g. a beam splitter) or active (e.g. an electronic quantum random number generator). In order to understand better the role of randomness in QKD we revisit the well-known "detector blinding" attack on BB84 QKD protocol, which utilizes strong light to achieve an undetectable and complete recovery of the secret key. We present two findings. First, we show that the detector blinding attack is in fact an attack on the receiver’s local entropy source. Second, based on this insight, we propose a modified receiver station and a statistical criterion which together enable robust detection of any bright-light attack and thus restore security.

Quantum amplitude estimation is a numerical integration technique and a candidate for the first operationally used quantum algorithm providing a quantum advantage in the NISQ era. Its main metric is the generated Fisher information per second, as it describes the accuracy of the numerical integration. The development of this metric can be coupled to the quantum volume of the used quantum processor with a phenomenological noise model. Since the increase of the quantum volume seems to follow an exponential pattern, insight in the integration power of quantum amplitude estimation for the upcoming years can be obtained. This shows that quantum amplitude estimation as a numerical integration technique will not provide an advantage for functions without significant improvements to the connectivity, reliability and speed of quantum processors. Beyond that, this method may be used the estimate the development of many more NISQ era algorithms.

In this work the author utilizes the quantum geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to Quantum Electrodynamics, and potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, that is compatible with the small value of the observed cosmological constant, and the breaking of matter-antimatter symmetry at high energies offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

The development of quantum computers seeks software developers' attention regarding security in the era of Information Technology, software security is the primary goal for our quantitative assessment of software security in the development cycle of software. Security assessment of software is identifying the key security factors of the software. A security elective provides ex-tensive strategies and calculations to ensure product safety. The security assessment is the key factor in surveying, administering, and controlling security to further enhance the nature of safety. It should be acknowledged that assessing security early on in the development process is beneficial in identifying worms, hazards, flaws, and threats. The definition and portrayal of Quantum Computing (QC) in software security will be discussed in this study. Researchers use cryptography calculations to secure our financial institutions, medical devices, military weaponry, planes, ships, vehicles, and pilots. Here authors of this study use the Fuzzy Technique for Order Preference by Similarity to Ideal Situation (FTOPSIS) to quantitatively assess the weight/rank of the quantum enable security alternatives like (Diffie-Hellman key-exchange algorithm, Quantum key distribution algorithm, Deutsch-Jozsa Algorithm, Special Deutsch-Jozsa Algorithm, Grover’s Algorithm and Quantum key distribution algorithm in GHZ state) with security factors like (Confidentiality, Integrity, Authenti-cation, Privacy, Reliability, Maintainability, Authorization, Integrity, Possessions, and Availability). Additionally, they critically analyze and select the six alternatives of quantum-based security algorithms. The nature of safety infers the ability to execute a thing on time in this exploration study, specifically 'software security'.

Moore’s law will cease to be relevant once transistors are the size of electrons. Once this occurs, we will no longer be able to use silicon for technological advancement. However, breakthroughs will continue in the form of a sixth paradigm: a 3D molecular computing model such as quantum comput- ing. Some of the promising areas of quantum computing researched in this study are (i) algorithmic advancements - such as Shor’s, Grover’s, error correction, fault tolerance and other new algorithms; (ii) hardware - such as the quantum system architecture, circuit models, entanglement, superposition and no-cloning qubits; (iii) market segments - such as finance, healthcare, and chemistry; (iv) the supremacy established over classical computing; and (v) areas of applicability. Significant progress has been made in these areas in recent decades, and they have garnered immense interest, attention and the funding required to make good progress.

Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum processors. Our results demonstrate that quantum computing of dynamical localization may become a convenient tool for evaluating advances in quantum hardware performances.

During the last 25 years the scientific community has coexisted with the most fascinating protocol due to Quantum Physics: quantum teleportation (QTele), which would have been impossible if quantum entanglement, so questioned by Einstein, did not exist. In this work, a complete architecture for the teleportation of Computational Basis States (CBS) is presented. Such CBS will represent each of the possible 24 classical bits commonly used to encode every pixel of a 3-color-channel-image (red-green-blue, or cyan-yellow-magenta). For this purpose, a couple of interfaces: classical-to-quantum (Cl2Qu) and quantum-to-classical (Qu2Cl) are presented with two versions of the teleportation protocol: standard and simplified.

In this paper, the connections between quantum non-locality and permutation symmetries are explored. This includes two types of symmetries: permutation across a superposition and permutation of qubits in a quantum system. An algorithm is proposed for nding the separability class of a quantum state using a method based on factorizing an arbitrary multipartite state into possible partitions, cyclically permuting qubits of the vectors in a superposition to check which separability class it falls into and thereafter using a reduced density-matrix analysis of the system is proposed. For the case of mixed quantum states, conditions for separability are found in terms of the partial transposition of the density matrices of the quantum system. One of these conditions turns out to be the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separability is also proposed. The concept of permutation of qubits is shown to be useful in dening a new entanglement measure in the `engle'.

In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

We present a model that incorporates the effect of two-body currents in quasielastic electron-nucleus scattering within the framework of a consistent superscaling formalism. This is achieved by defining an averaged single-nucleon hadronic tensor based on the 1p1h matrix element of the one-body current plus meson-exchange currents (MEC). The consistent treatment of one- and two-body currents in our model enables the calculation of exchange current effects in the kinematical region where the Fermi gas response is zero, but not the scaling function. The effect of MEC is consistently taken into account when extracting the phenomenological scaling function from electron scattering data. With this model, we investigate the effect of MEC on the response functions taking into account the effective mass of the nucleon, and examine the consequences it has on the inclusive (e,e′) cross section. We find that 1p1h MEC deplete the quasielastic transverse response, while they not alter significantly the scaling behavior of (e,e′) data.

Here we use the flat Friedmann-Lemaitre-Robertson-Walker metric describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the astrophysical literature. We use the co-moving coordinate r_e (the subscript e indicates emission) for the place of a galaxy which is emitting photons and r_a (the subscript a indicates absorption) for the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the real physical distance - the way of light - is calculated by D = a(t₀) r_a - a(t_e) r_e. Here means a(t₀) the today’s (t₀) scale parameter and a(t_e) the scale parameter at the time of emission (t_e) of the photons. Nobody can doubt this real travel way of light: The photons are emitted on the co-moving coordinate place r_e and are than traveling to the co-moving coordinate place r_a. During this traveling the time is moving from t_e to t₀ (t_e ≤ t₀) and therefore the scale parameter is changing in the meantime from a(t_e) to a(t₀). Using this right way of light we calculate some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics. As one result we get e.g. the today’s Hubble parameter H_0a ≈ 62.34 km/(s Mpc). This value is smaller than the Hubble parameter H_0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data [12] which is discussed in the literature.

Motivated by the well-known contradiction of special relativity and the heat equation, a wave equation for temperature scalar field is presented that also resolves the old controversy of (Lorentz) transformation of temperature and entropy. After showing that the current dogma of temperature and entropy being emergent concepts is based on but a logical fallacy, it is proposed that single particles posses entropy. This principle of fundamentality of entropy is then shown to be compatible with the equipartition theorem by yielding corrections in the quantum gravity regime.

The non-inertial effects on spin-0 scalar particle that interacts with scalar potentials of Cornell-type in cylindrical system and Coulomb-type in the magnetic cosmic string space-time using Kaluza-Klein theory is analyzed. We show that the energy eigenvalue and eigenfunction depend on the global parameters characterizing the space-time, and the gravitational analogue of the Aharonov-Bohm effect for bound states is observed.

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the $1h1p$ sector) in heavy atoms (Xe, Hg) and simple molecules of heavy element compounds (I${}_2$, TlF) are reported.

(3+1)D quantum mechanics is a four-dimensional quantum formalism, which is developed neither in a Minkowski spacetime, nor in a purely Hilbert space and not its metric is Lorentzian. This quantum mechanics also yields the quantum Einstein field equation in (3+1)D quantum spacetime. Every observable (3+1)D quantum spacetime can be found to contain internally hidden opposite spin quantum state, that results Supersymmetry. Closed continuous mappings of this hidden quantum state immediately yield more extra hidden dimensions including string. This string is found to be fundamentally eleven-dimensional (rather than lower dimensional) by nature within this quantum spacetime, which is necessarily a natural phenomenon of (3+1)D Quantum Mechanics.

The double nature, wave and corpuscular, of the material particles is usually considered incomprehensible as it cannot be represented visually. It is proposed to the student, in the introductory courses, as a fact justified by quantum interference experiments of which, however, no further analysis is possible. In this note we propose a description of the wave function in terms of a simple electrical analogy, which reproduces at least some of its essential properties. The aim we propose is to provide a cognitive representation of an analogical type: starting from a classical context (electrical circuits) and introducing in an appropriate way the notions of "wave" and "particle", we show how typically quantum properties such as delocalization and entanglement emerge in a natural, understandable and intuitive way.

Quantum mechanics is often described as irreducibly non-local. A tacit element of this picture is the assumption that one and the same sub-ensemble of quanta is post-selected in every measurement combination of a Bell test. Yet, this expectation was recently shown to be formally inconsistent with quantum theory (Cetto et al., 2020) and even to be experimentally falsifiable (Mardari 2021). The need to make sense of this development motivated a rigorous conceptual analysis of quantum non-locality, especially as it relates to the basic principles of quantum mechanics. The simple conclusion is that quantum theory and quantum non-locality are fundamentally incompatible. This is not a loophole around the predictions of quantum mechanics, but rather an insight into the essential conditions that make them accurate.

In recent years, the term quantum-like has been increasingly used in different disciplines, including neurosciences, psychological and socio-economical disciplines, claiming that some investigated phenomena show “something” in common with quantum processes and, therefore, they can be modeled using a sort of quantum formalism. Therefore, the increasing use of the term quantum-like calls for defining and sharing its meaning in order to properly adopt it and avoid possible misuse. In our opinion, the concept of quantum-like may be successfully applied to macroscopic phenomena and empirical sciences other than physics when at least two conditions are satisfied: a) the behavior of the investigated phenomena show logical analogies with quantum ones; b) it is possible to find a criterion of truth based on an experiential/scientific approach applied to a probabilistic model of description of the phenomena. This is only a first, small step in the approach to the concept of quantum-like, hopefully helpful to promote further discussion and achieve a better definition.

In this paper, I propose new models of quantum information processing using the exchange interaction in physical systems. The partial SWAP operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherence-free subspaces. Given the non-commutativity of these operators (for adjacent operators operating on a common qubit), a number of quantum states and entanglement patters can be obtained. This zoo of states can be classified, due to the parity constraints and permutation symmetry of the states, into invariant subspaces that are used for the definition of some of the applications in this paper.

Quantum Computation, in the gate array version, uses logical gates adopting convenient forms for computational algorithms based on those of classical computation. There, two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite, their design depends on specific quantum systems and physical interactions involved, exacerbating the dynamics analysis. Predictable and controllable manipulation should be addressed to control the quantum states, but resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in SU(2^2d) for 2d-partite two-level systems into 2^2d-1 SU(2) quantum subsystems. Decomposition lets to set control procedures, to generate large entangled states and to design specialized dedicated quantum gates. There, easy and traditional operations proposed by quantum computation are recovered for more complex and large systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the generalized Bell states basis. It could be understood as a momentary splitting of the 2d information channels into 2^2d-1 pairs of 2 level quantum information subsystems and a settlement of the quantum information manipulation free of the imposed restrictions by the underlying physical system.

Silica on Silicon is a major optical integration platform, while the emergent class of integrated Laser written circuits' platform offers additionally high customizability, and flexibility for rapid prototyping. However, the inherent waveguides' low core/cladding refractive index contrast characteristic compared to other photonic platforms in silicon or silicon nitride, sets serious limitations for on-chip efficient coupling with single photon emitters, like semiconductor nanowires with quantum dots limiting the applications in quantum computing. A new light coupling scheme proposed here overcomes this limitation providing means for light coupling >50%. The scheme is based on the incorporation of an optical microsphere between the nanowire and the waveguide, properly optimized and arranged in terms of: size, refractive index, distance of microsphere between nanowire and waveguide. Upon suitable design of the optical arrangement, the photonic nanojet emitted by the illuminated microsphere excites efficiently the guided eigenmodes of the input channel waveguide, thus launching light with high coupling efficiency. The method is tolerant in displacements, misalignments, and imperfections and is fabricationally feasible by current state of the art techniques. The proposed method enables the on-chip multiple single photon emitters' integration thus allowing the development of highly customizable and scalable quantum photonic integrated circuits for quantum computing.

Quantum image representation is a widely researched area of quantum computing. Currently developed methods use angle parameter of the rotation gate (e.g., the FRQI method), sequences of qubits (ex. NEQR method) or phase shift (ex. LPIQE method) for storing color information of pixels. All of those methods are affected by decoherence and other classical and quantum noise, which is an inseparable part of quantum computing in a NISQ (Noisy Intermediate Scale Quantum) era. These all phenomenons influence the measurements, its probability distribution over the measurement basis and, as the result, makes the extracted images not even similar to those, which was stored in quantum computers. Since this process is, in its foundation, quantum as well, the computational reversal of this process is possible. There are a lot of methods for error correction, mitigation and reduction, but all of them use quantum computer time, or additional qubits to achieve desired result. We report a successful use of the Generative Adversarial Network tuned for image-to-image translation in conjunction with PDU method, for error reduction in images encoded using LIPQE (Local Phase Image Quantum Encoding) method.

We propose a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions. Nonclassical states of light are an essential resource for high precision optical techniques that rely on photon correlations and noise reshaping. Notable techniques include quantum enhanced interferometry, ghost imaging, and generating fault tolerant codes for continuous variable optical quantum computing. We show that a class of nonlinear-optical resonators can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon number dependent frequency matching, inducing photon number selective interactions. With a high amplitude coherent pump, the number selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing, illustrated with simulations. We specify the requisite material properties to build the device and highlight the remaining material degrees of freedom which offer flexible material design.

We consider new insights into the origin and nature of pointer states and their role in wave function collapse in macroscopic quantum coherence. The work includes new theory of quantum coherence underpinned by turbulence, generated by a field of pointer states in the form of recirculating vortices (toroids), interconnected via a vortex cascade. Decoherence occurs when the interconnected field of vortices between pointer states is disrupted by external forces, leading to their localisation. The applicability of this work is considered in addressing unresolved questions in high temperature superconductivity and macroscopic quantum processes in biological systems. We also consider its implications for our understanding of intrinsic spin and pointer states within the standard "point source" representation of a quantum particle, which intuitively requires a more complexed description.

Having access to a unique quantum circuit that one wants to protect against use by others is a very likely scenario. However currently users rely on classical computer security schemes, which have known shortcomings. In this chapter we introduce a novel protection scheme along with a survey of other known methods to protect quantum information. In particular we review physically unclonable functions (PUFs), obfuscation, and introduce quantum logic locking.

A cyclic antipodal points of a circle is a pair of points that are the intersection of the circle with a diameter of the circle. A recent proof of Ptolemy’s Theorem, simultaneously in both (i) Euclidean geometry; and (ii) the relativistic model of hyperbolic geometry (which is identified with the Klein model of hyperbolic geometry), motivates in this article the study of four cyclic antipodal points of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Formulas that extend the Pythagorean formula in both Euclidean and hyperbolic geometry are obtained as byproducts

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. For such supersymmetric Hamiltonians an exact Foldy-Wouthuysen transformation exits which brings it into a block-diagonal form separating the positive and negative energy subspaces. Here the supercharges transform between energy eigenstates of positive and negative energy. The relativistic dynamics of a charged particle in a magnetic field is considered for the case of a scalar (spin-zero) boson obeying the Klein-Gordan equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation.

Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron-electron interactions and one-loop quantum electrodynamics effects. Here we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac-Coulomb and Dirac-Coulomb-Gaunt Hamiltonians.

Quantum entanglement is a fascinating topic with both theoretical and technological impacts. Yet, even in the simplest scenarios, there are still various open questions involving pure state and mixed state entanglement. Here we present the simplest entangled mixed states. We consider both qubits (quantum bits) and qudits (quantum digits). We first provide our simplest yet most important result for rank-2 bi-partite states, and we then generalize our results to go beyond rank-2 and to go beyond bi-partite states.

The goal of finding a commutative group of gates from the set of unitary matrices is to simplify the process of quantum computing. If a set of gates is commutative, then we can apply the gates in any order without affecting the final outcome. This is important because quantum systems are very sensitive to errors and decoherence, and any disruption to the system can cause errors in the computation.By having a commutative group of gates, we can simplify the process of designing quantum algorithms and reduce the risk of errors. This is particularly important for solving complex computational problems that cannot be solved by classical computers.

Tremendous progress has been witnessed in artificial intelligence within the domain of neural network backed deep learning systems and its applications. As we approach the post Moore’s Law era, the limit of semiconductor fabrication technology along with a rapid increase in data generation rates have lead to an impending growing challenge of tackling newer and more modern machine learning problems. In parallel, quantum computing has exhibited rapid development in recent years. Due to the potential of a quantum speedup, quantum based learning applications have become an area of significant interest, in hopes that we can leverage quantum systems to solve classical problems. In this work, we propose a quantum deep learning architecture; we demonstrate our quantum neural network architecture on tasks ranging from binary and multi-class classification to generative modelling. Powered by a modified quantum differentiation function along with a hybrid quantum-classic design, our architecture encodes the data with a reduced number of qubits and generates a quantum circuit, loading it onto a quantum platform where the model learns the optimal states iteratively. We conduct intensive experiments on both the local computing environment and IBM-Q quantum platform. The evaluation results demonstrate that our architecture is able to outperform Tensorflow-Quantum by up to 12.51% and 11.71% for a comparable classic deep neural network on the task of classification trained with the same network settings. Furthermore, our GAN architecture runs the discriminator and the generator purely on quantum hardware and utilizes the swap test on qubits to calculate the values of loss functions. In comparing our quantum GAN, we note our architecture is able to achieve similar performance with 98.5% reduction on the parameter set when compared to classical GANs. With the same number of parameters, additionally, QuGAN outperforms other quantum based GANs in the literature for up to 125.0% in terms of similarity between generated distributions and original data sets.

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum $ P(k) $ and the CMB temperature angular power spectrum $ C_l $’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients $ C_l $, which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.

Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than fully-connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multi-features in multidimensional data. In this paper, we present a multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multi-feature quantum convolution with average and Euclidean pooling and thus adapting the CNN structure to a variational quantum algorithm (VQA). Average pooling is based on the quantum Haar transform (QHT) and Euclidean pooling is based on partial quantum measurement. The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results showed favorable characteristics of our proposed techniques compared to existing work with respect to a number of quantitative metrics such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count.

Atomtronics is a relatively new subfield of atomic physics that aims to realize the device behavior of electronic components in ultracold atom-optical systems. The fact that these systems are coherent makes them particularly interesting since, in addition to current, one can impart quantum states onto the current carriers themselves or perhaps perform quantum computational operations on them. After reviewing the fundamental ideas of this subfield, we report on the theoretical and experimental progress made towards developing externally-driven and closed loop devices. The functionality and potential applications for these atom analogs to electronic and spintronic systems is also discussed.

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured at the same time. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level.

Classic game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the Prisoner's Dilemma (PD), have attracted a lot of attention. Similarly, state machines and specifically finite automata have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine some well-known game conditional strategies that have been studied within the framework of the repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with probability 1, achieving some interesting results. We also study the quantum version of PD under the Eisert-Wilkens-Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

Considering the predictions from the standard model of particle physics coupled with experimental results from particle accelerators, we discuss a scenario in which from the infinite possibilities in the Lie groups we use to describe particle physics, nature needs only the lower dimensional representations - an important phenomenology that we argue indicates nature is code theoretic. We show that the quantum deformation of the SU(2) Lie algebra at the fifth root of unity can be used to address the quantum Lorentz group representation theory through its universal covering group and gives the right low dimensional physical realistic spin quantum numbers confirmed by experiments. In this manner we can describe the spacetime symmetry content of relativistic quantum fields in accordance with the well known Wigner classification. Further connections of the fifth root of unity quantization with the mass quantum number associated with the Poincaré Group and the SU(N) charge quantum numbers are discussed as well as their implication for quantum gravity.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.