In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.

In this paper we use the additive thermodynamic formalism to obtain new bounds of the Hausdorff and box-counting dimension of certain non conformal hyperbolic repellers defined by piecewise smooth expanding maps on a $d$-dimensional smooth manifold $M$.

In this paper, we investigate how Rindler observer measures the universe in the ADM formalism. We compute his measurements in each slice of the space-time in terms of gravitational red-shift which is a property of general covariance. In this way, we found special relativity preferred frames to match with the general relativity Rindler frame in ADM formalism. This may resolve the widely known incompatibility between special relativity and general relativity on how each theory sees the red-shift. We found a geometric interpretation of the speed of light and mass.

We discuss a possible scale of gravitational origin at around 10 MeV, or 10⁻¹² cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago.~A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of 10⁻¹² cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of ~10¹²⁰ multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to 1–2 MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.

The recently proposed Holography-inspired approach to quantum gravity is reviewed and expanded. The approach is based on the foliation of the background spacetime and reduction of the offshell states to the physical states. Careful attention is paid to the boundary conditions. It is noted that the outstanding problems such as the cosmological constant problem and black hole information can be tackled from the common thread of the quantized gravity. One-loop renormalization of the coupling constants and the beta function analysis are illustrated. Active galactic nuclei and gravitational waves are discussed as the potential applications of the present quantization scheme to astrophysics.

We propose a quantum version of the well known minimum distance classification model called "Nearest Mean Classifier" (NMC). In this regard, we presented our first results in two previous works. In [34] a quantum counterpart of the NMC for two-dimensional problems was introduced, named "Quantum Nearest Mean Classifier" (QNMC), together with a possible generalization to arbitrary dimensions. In [33] we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding of n-dimensional patterns into density operators is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted to: i) compare the NMC and QNMC performance on different datasets; ii) study the effects of the non-invariance under uniform rescaling for the QNMC.

This study mainly explores the effect of policy formalism, equipment insufficiency, covid-19 fear and job insecurity on construction workers’ insomnia during the epidemic. The main contribution of this article is to introduce policy formalism into the exploration of the causes of insomnia among construction site workers during the epidemic. This study collected 733 valid samples of construction site workers. We tested the established hypotheses using confirmatory factor analysis and structural equation modeling. The research results found that equipment insufficiency positively affects Covid-19 fear. Policy formalism and Covid-19 fear positively affect job burnout. Social support negatively affects job burnout. Job burnout and job insecurity positively affect insomnia.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

The ability to simulate realistically the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulations aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the size of the superconducting order parameter.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

Chronology unprotected mechanisms are considered with a very low gravitational polarization to make the wormhole traversal with positive energy density everywhere. No need of exotic matter has been considered with the assumption of the Einstein-Dirac-Maxwell Fields, encountering above the non-zero stress-energy-momentum tensor through spacelike hypersurfaces by a hyperbolic coordinate shift.

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

After developed the formulation of a "general relativity" in C⁴ [2], we proceed with the formulation of a Hamilton-Jacobi equation in C⁴. We argue that in this consideration, the usual problems of the ADM formalism, do not exist, due to the complex time as it exists in our consideration. Specically, we can derive a suitable dispersion relation in order to work with and nd a generalised super Hamiltonian

This is a short introductory review on quantum-like modeling of cognition with applications to decision making and rationality. The aim of the review is twofold: a) to present briefly the apparatus of quantum information and probability theory useful for such modeling; b) to motivate applications of this apparatus in cognitive studies and artifical intelligence, psychology, decision making, social and political sciences. We define quantum rationality as decision making that is based on quantum information processing. Quantumly and classically rational agents behaves differently. A quantum-like agent can violate the Savage Sure Thing Principle, the Aumann theorem on impossibility of agreeing to disagree.Such an agent violates the basic laws of classical probability, e.g., the law of total probability and the Bayesian probability inference. In some contexts, ``irrational behavior'' (from the viewpoint of classical theory of rationality) can be profitable, especially for agents who are overloaded by a variety of information flows. Quantumly rational agents can save a lot of information processing resources. At the same time, this sort of rationality is the basis for quantum-like socio-political engineering, e.g., social laser. This rationality plays the important role in the process of decision making not only by biosystems, but even by AI-systems. The latter equipped with quantum(-like) information processors would behave irrationally, from the classical viewpoint. As for biosystems, quantum rational behavior of AI-systems has its advantages and disadvantages. Finally, we point out that quantum-like information processing in AI-systems can be based on classical physical devices, e.g., classical digital or analog computers.

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of scienThe Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.ce, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

A relationship between the functional Schr\"odinger representation and the precanonical quantization of a nonlinear scalar field theory is extended to arbitrary curved space-times. The canonical functional derivative Schr\"odinger equation is derived from the manifestly covariant precanonical Schr\"odinger equation in a singular limiting case when the ultraviolet parameter $\varkappa$ introduced by precanonical quantization is identified with the invariant delta-function at equal spatial points. In the same limiting case, the Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration. Thus the standard QFT in curved space-time in functional Schr\"odinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

In this paper we will consider the cosmic fluid to be dissipating i.e it has both bulk and shearing viscosity. We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for cosmic fluid which is dissipating i.e it has both shearing and bulk viscosity. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion of Bianchi type 1 in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. By this transformation we can express the mass to be moving in a scalar potential field. This definition helps us to explain the nature of expansion of universe during cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved. In the case of bulk and shearing viscous fluid we get the solution of damped harmonic oscillator after the cosmological inflation.Part I contains the calculations of bulk viscous fluids and Part II contains the calculations of bulk and shearing viscous fluid.At the end we have also provided the relation of shearing and expansion.Part III will give the approximation of low viscosity to solve the viscous fluid problem.

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Terms related to gradients of scalar fields are introduced as scalar products into the formulation of entropy. A Lagrange density is then formulated by adding constraints based on known conservation laws. Applying the Lagrange formalism to the resulting Lagrange density leads to the Poisson equation of gravitation and also includes terms being related to curvature of space. The formalism further leads to terms possibly explaining nonlinear extensions known from modified Newtonian dynamics approaches. The article concludes with a short discussion of the presented methodology and provides an outlook on other phenomena, which might be tackled using this new approach.

The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to the stable MG1 queue manifold. More potentially, both service time probability and cumulative functions which make KLDF exact are obtained. The credibility of KLDF is justified through consistency axioms. Some potential applications of Kullback-Leibler divergence to Biometry are presented. The paper concludes with closing remarks combined with some challenging open problems and the next phase of research.

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.