ARTICLE | doi:10.20944/preprints202211.0277.v2
Subject: Physical Sciences, General & Theoretical Physics Keywords: physical system; attraction; repulsion; Ramsey theory; transitivity; complete graph; dipole-dipole interaction; relativity; Hamiltonian path.
Online: 20 January 2023 (07:50:16 CET)
Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of the behavior of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.
ARTICLE | doi:10.20944/preprints201808.0167.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: graphene grain boundaries; scattering matrix theory; dirac hamiltonian
Online: 8 August 2018 (12:20:13 CEST)
The implementation of graphene-based electronics requires fabrication processes able to cover large device areas since exfoliation method is not compatible with industrial applications. Chemical vapor deposition of large-area graphene represents a suitable solution having the important drawback of producing polycrystalline graphene with formation of grain boundaries, which are responsible for limitation of the device performance. With these motivations, we formulate a theoretical model of graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the particle transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach and represents per se an important enrichment of the scattering theory of graphene. Moreover, the outcomes of the theory can contribute in understanding and limiting detrimental effects of graphene grain boundaries also providing a benchmark for more elaborated techniques.
Subject: Physical Sciences, Applied Physics Keywords: metamaterial; hyperbolic metamaterial; Drude Model; Lorentz Model; Lagrangian; Hamiltonian
Online: 20 July 2020 (09:00:54 CEST)
In this work, we study the dynamical behaviors of the electromagnetic fields and material responses in the hyperbolic metamaterial consisting of periodically arranged metallic and dielectric layers. The thickness of each unit cell is assumed to be much smaller than the wavelength of the electromagnetic waves, so the effective medium concept can be applied. When electromagnetic (EM) fields are present, the responses of the medium in the directions parallel to and perpendicular to the layers are like that of Drude and Lorentz media, respectively. We derive the energy density of the EM fields and the power loss in the effective medium based on Poynting theorem and the dynamical equations of the polarization field. We also show that the Lagrangian density of the system can be constructed. The Euler-Lagrangian equations yield the correct dynamical equations of the electromagnetic fields and the polarization field in the medium. The canonical momentum conjugates to every dynamical field can be derived from the Lagrangian density via differentiation or variation with respect to that field. We apply Legendre transformation to this system, and find that the resultant Hamitonian density is identical to the energy density, up to an irrelevant divergence term.
ARTICLE | doi:10.20944/preprints201608.0238.v1
Subject: Materials Science, Nanotechnology Keywords: anisotropic exchange; single molecule magnets; Spin Hamiltonian; CASSCF; NEVPT2
Online: 31 August 2016 (10:56:43 CEST)
The rationalization of single molecule magnets’ (SMMs) magnetic properties by quantum mechanical approaches represents a major task in the field of the Molecular Magnetism. The fundamental interpretative key of molecular magnetism is the phenomenological Spin Hamiltonian and the understanding of the role of its different terms by electronic structure calculations is expected to steer the rational design of new and more performing SMMs. This paper deals with the ab initio calculation of isotropic and anisotropic exchange contributions in the Fe(III) dimer [Fe2(OCH3)2(dbm)4]. This system represents the building block of one of the most studied Single Molecule Magnets ([Fe4RC(CH2O)3)2(dpm)6] where R can be an aliphatic chain or a phenyl group just to name the most common functionalization groups) and its relatively reduced size allows the use of a high computational level of theory. Calculations were performed using CASSCF and NEVPT2 approaches on the X-ray geometry as assessment of the computational protocol, which has then be used to evinced the importance of the outer coordination shell nature through organic ligand modelization. Magneto-structural correlations as function of internal degrees of freedom for isotropic and anisotropic exchange contributions are also presented, outlining for the first time the extremely rapidly changing nature of the anisotropic exchange coupling.
ARTICLE | doi:10.20944/preprints202109.0061.v1
Subject: Physical Sciences, Fluids & Plasmas Keywords: Hamiltonian dynamics; Adiabatic invariants; Magnetized plasma; Particle trajectory; Canonical transformations
Online: 3 September 2021 (11:26:19 CEST)
The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic–although possibly incommensurate–motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet–to our knowledge–such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle’ orbit without the need to pass through the hourly law of motion.
ARTICLE | doi:10.20944/preprints202104.0254.v1
Subject: Physical Sciences, Mathematical Physics Keywords: entanglement entropy; local Hamiltonian; many-body localization; quantum dynamics; volume law
Online: 9 April 2021 (10:16:52 CEST)
In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].
ARTICLE | doi:10.20944/preprints201709.0091.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: Hamiltonian systems; classical statistical mechanics; ensemble equivalence; long-range interacting systems
Online: 20 September 2017 (04:08:44 CEST)
We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.
ARTICLE | doi:10.20944/preprints202206.0221.v9
Subject: Physical Sciences, General & Theoretical Physics Keywords: general relativity; cosmology; continuum mechanics; fluid dynamics; field theory; electrodynamics; Hamiltonian mechanics
Online: 29 November 2022 (03:59:30 CET)
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system with an electromagnetic field, leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress-energy tensor expresses relativistic Cauchy's momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.
SHORT NOTE | doi:10.20944/preprints202209.0163.v1
Subject: Physical Sciences, Nuclear & High Energy Physics Keywords: special relativity; general relativity; covariant electromagnetism; Lagrangian formulation; Hamiltonian; loop quantum gravity
Online: 13 September 2022 (08:01:05 CEST)
Loop quantum gravity (LQG) quantizes gravity through the quantization of the space-time. It begins with general relativity (GR) and brings some concepts from quantum field theory to quantize the space-time. The conceptual background of GR is necessary to comprehend the LQG framework. Therefore, in this paper, prerequisite concepts such as special relativity, general relativity, covariant electromagnetism, tensor analysis, Lagrangian formulation, Hamiltonian formulation and basics of quantum mechanics are briefly introduced; that, are needed to study loop quantum gravity(LQG).
ARTICLE | doi:10.20944/preprints202002.0302.v1
Subject: Social Sciences, Economics Keywords: tobacco smoking; intention to quit smoking; Hamiltonian Monte Carlo; Bayesian analysis; Zambia
Online: 21 February 2020 (03:14:01 CET)
The tobacco epidemic is one of the leading public health threats the world has ever faced and public health policy that seeks to limit the problem may not only have to target the price of tobacco but also the initiation stage in a smoker’s life – the adolescent stage. This research contributes to the health economics literature by using a Bayesian hierarchical logistic model, estimated using Hamiltonian Monte Carlo (HMC) methods to empirically identify what drives the intentions to quit smoking among adolescent smokers in Zambia. Results suggest that among the junior secondary school-going adolescent smokers in Zambia, about 63% have plans to quit smoking. We find socio-demographic characteristics and several tobacco-smoking-related factors as the main drivers of adolescent smokers’ plans to quit smoking. Most importantly, we provide insights that could be useful to help adolescent smokers realize their quitting plans.
Subject: Engineering, Control & Systems Engineering Keywords: hybrid energy storage system; L2-gain disturbance attenuation; passivity-based control; port-controlled Hamiltonian model
Online: 16 April 2020 (06:36:09 CEST)
Battery/Supercapacitor(SC) current tracking control is a key issue for hybrid energy storage system (HESS) in electric vehicles. An innovative passivity-based L2-gain adaptive control (PBL2AC) based on port-controlled Hamiltonian model with dissipativity (PCHD) for reference current tracking and bus voltage stability in HESS is presented. The developed PCHD model has considered both parameter variations and external disturbances. By using L2-gain disturbance attenuation, the PBL2AC ensures robust reference current tracking and stable bus voltage. Moreover, adaptive mechanism is adopted to estimate the electrical parameters. To validate the proposed control scheme for HESS, simulations and experiments were done and compared with traditional PID and sliding mode control under several typical driving cycles, and results show that the effectiveness of the proposed controller can be confirmed.
ARTICLE | doi:10.20944/preprints202105.0369.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: personality dynamics; general factor of personality; stimulus-response model; minimum action principle; Hamiltonian; Ermakov-Lewis energy
Online: 17 May 2021 (07:56:34 CEST)
The objective of this paper is to present a mathematical formalism that states a bridge between Physics and Psychology, concretely between analytical dynamics and personality theory in order to open new insights in this theory. In this formalism energy plays a central role. First, the short-term personality dynamics can be measured by the General Factor of Personality (GFP) response to an arbitrary stimulus. This GFP dynamical response is modelled by a stimulus-response model: an integro-differential equation. The bridge between Physics and Psychology is provided when the stimulus-response model can be formulated as a linear second order differential equation and, subsequently, reformulated as a Newtonian equation. This bridge is strengthened when the Newtonian equation is derived from a minimum action principle, obtaining the current Lagrangian and Hamiltonian functions. However, the Hamiltonian is a non-conserved energy. Then, some changes provide a conserved Hamiltonian function: the Ermakov-Lewis energy. This energy is presented, as well as the GFP dynamical response that can be derived from it. An application case is presented: an experimental design in which 28 individuals consumed 26.51 g of alcohol. This experiment provides an ordinal scale for the Ermakov-Lewis energies that predicts the effect of a single dose of alcohol.
Subject: Physical Sciences, Condensed Matter Physics Keywords: solids; quantum linear harmonic oscillator; classical linear oscillator; partition function; Hamiltonian; position fluctuations; Hamilton function; thermodynamic properties
Online: 19 June 2019 (08:06:19 CEST)
As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.
ARTICLE | doi:10.20944/preprints202108.0375.v1
Subject: Social Sciences, Political Science Keywords: availability; cipher coding; clogged water; honeycomb tori; maintainability; mutually independent Hamiltonian paths (MIHP); interference; privacy; reliability; wicked problems
Online: 18 August 2021 (11:22:39 CEST)
Holistic information integrity for managing wicked problems, developing equity is getting attention. Artifitial intelligence based topologies, dual sensor-information nodes, are prototyped to offer more availability, reliability, maintainability for operating healthy urbanism. Bipartite spider-webs, cube-connected cycles are aimed in ‘the radial-ring urban-building skeleton’ and ‘wetlands and sparsely populated areas’, respectively. Furthermore, honeycomb tori, mathematical HT(m), m≥2, for tasks related to wireless communications, are found having two mutually independent Hamiltonian paths (MIHP). This parallelism creates dual cipher-coding, supports logistic privacy, and help prevent information loss, electromagnetic interference, unexpected changes caused by such as clogged water.
ARTICLE | doi:10.20944/preprints201911.0097.v1
Subject: Keywords: quantum field theory in curved space-time; De Donder-Weyl Hamiltonian formalism; precanonical quantization; canonical quantization; functional Schrödinger representation
Online: 8 November 2019 (11:04:19 CET)
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.
ARTICLE | doi:10.20944/preprints202101.0146.v1
Subject: Keywords: General theory of relativity; Bianchi type 1; Hamiltonian formalism; bulk viscosity; cosmology; Fluid dynamics; Isotropic and Anisotropic cosmology; shearing viscosity
Online: 8 January 2021 (11:21:41 CET)
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.
ARTICLE | doi:10.20944/preprints202005.0083.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: nonrelativistic QED; many-body theories; Lagrangian; gauge invariance; Coulomb gauge; Hamiltonian; external fields; quantization; 1/c2 approximation; current-current interaction
Online: 5 May 2020 (15:14:06 CEST)
We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.
ARTICLE | doi:10.20944/preprints202107.0685.v1
Subject: Physical Sciences, Acoustics Keywords: Physics, Helmholtz Hamiltonian Mechanics, stringmetrics, Electromagnetism, Pauli Dirac Planck circuit like monopole particle assembly, Gage, asymmetric\strings\gage\metrics, Transforms, SUSY, Quantum Astrophysics.
Online: 30 July 2021 (09:20:05 CEST)
This article will continue ansatz gage matrix of Iyer Markoulakis Helmholtz Hamiltonian mechanics points’ fields gage to Pauli Dirac monopole particle fields ansatz gage general formalism at Planck level, by constructing a Pauli Dirac Planck circuit matrix field gradient of particle monopole flow loop. This circuit assembly gage (PDPcag) that maybe operating at the quantum level, demonstrates the power of point fields matrix theoretical quantum general formalism of Iyer Markoulakis Helmholtz Hamiltonian mechanics transformed to Coulomb gage metrics, to form eigenvector fields of magnetic monopoles as well as electron positron particle gage metrics fields. Eigenvector calculations performed based on Iyer Markoulakis quantum general formalism are substituted for gage values of typical eigenvectors of dipolar magnetically biased monopoles with their conjugate eigenvectors, as well as eigenvector fields that are of the electron and positron particles. Then they are compiled to form combinatorial eigenvector matrix bundle of the monopole particle circuit field constructs assembly. Evaluation of this monopole particle fields matrix provided eigenvector fields results like SUSY, having Hermitian quantum matrix with electron-positron annihilation alongside north and south monopoles collapsing to dipolar “stable” magnetism, representing electromagnetic gaging typical metrics fields. Applying experimental observations on magnetic poles with measuring magnetic forces John Hodge’s results were showing asymmetrical pole forces; author has mathematically constructed asymmetric\strings\gage\metrics to characterize electromagnetic gravity, putting together while integrating with stringmetrics gravity that author has been reporting in earlier published articles. Physical Analysis with generalization of mass-charge and charge-fields gage metrics to quantum relativity gage metrics fields are proposed based on author’s proof formalism paper providing derivational algorithmic steps, to determine gage parametric values within the equation of Coulomb gage. Vortex fields’ wavefunctions and the scalar potential characterized by a function and a coupling constant having quantum density matrix together define the gage metrics quantifiable observable measurement physics of electron-positron cross-diagonal fields; contrastingly, diagonal terms of PDPcag matrix characterizes electron-positron particle eigenvector fields, while Hilbert Higgs mass metrics characterizes eigen-matter. Author is already working with Christopher O’Neill about magic square symmetry configurations to quantitatively understand symmetry, structure, and the real space geometry that are expected to form out of vacuum quanta point fields’ quantitative quantum general formalism theory of Iyer Markoulakis. In addition, author is currently collaborating with Manuel Malaver’s astrophysical Einstein Minkowski modified space time metrics evaluations of the sense-time-space relativistic general metrics to have means to account for curving or shaping of spacetime topology of a five-dimensional sense-time-space. Manuel Malaver’s specialization with modified Einstein Maxwell equations for modeling galaxies and stars cosmological physics, utilizing Einstein-Maxwell-Tolman- Schwarzschild and Reissner-Nordström spacetime and black holes theoretical formalisms have author of this paper collaboratively model quantum astrophysics of dark energy Star’s theory with Einstein-Gauss-Bonnet gravity equations.
ARTICLE | doi:10.20944/preprints202205.0327.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: Wave-black hole duality; nonmetricity; corrections to gravitational potential; minimum gravitational potential; geometry of implicit line elements; corrected Schwarzschild metric; energy-momentum tensor of spacetime; wavefunction of a black hole; Hamiltonian dynamics of a manifold; tensor Poisson bracket
Online: 24 May 2022 (09:30:41 CEST)
There is no formal difference between particles and black holes. This formal similarity lies in the intersection of gravity and quantum theory; quantum gravity. Motivated by this similarity, `wave-black hole duality' is proposed, which requires having a proper energy-momentum tensor of spacetime itself. Such a tensor is then found as a consequence of `principle of minimum gravitational potential'; a principle that corrects the Schwarzschild metric and predicts extra periods in orbits of the planets. In search of the equation that governs changes of observables of spacetime, a novel Hamiltonian dynamics of a Pseudo-Riemannian manifold based on a vector Hamiltonian is adumbrated. The new Hamiltonian dynamics is then seen to be characterized by a new `tensor bracket' which enables one to finally find the analogue of Heisenberg equation for a `tensor observable' of spacetime.