Class Of Particle Systems Research Articles

Divergent features of collective gravitational quantum excitations

In this research, we study different aspects of collective gravitational quantum excitations in the framework of the quantum multistream model. The energy dispersion of collective electrostatic (plasmon) and gravitational excitations or as we call gravity quasiparticle (GQ) are derived using the nonrelativistic and relativistic models and many parameters such as the effective mass, phase, and group speed of quasiparticle excitations are studied, in detail. It is shown that, unlike plasmons with a forbidden energy gap, all positive and negative energy values are allowed for GQs. However, unlike plasmon with a dual-tone nature of collective excitations, the GQs are found to be single-tone with either wave-like or particle-like oscillations being strongly damped. The linear phase-space evolution of GQs indicates that they evolve similarly to the classical system of particles in the center of the mass frame in which the force due to self-consistent gravitational potential plays the role of interparticle forces. It is shown that the damping of wavelike or particle-like excitations in GQ energy dispersion leads to three distinct phenomena of gravitational expansion (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E>0$$\\end{document}), stable matter (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E=0$$\\end{document}) and gravitational collapse (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E<0$$\\end{document}), respectively. The Hubble-Lemaitre-like relation is obtained from the generalized probability current for GQs. The quantum gravitational interference effect is also studied.

Simulations of classical three-body thermalization in one dimension.

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V_{ij}∝1/|x_{i}-x_{j}|^{n} or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equationto evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ^{2}T^{1/2-1/n}, where ρ is the number density. The corresponding proportionality constant decreases with increasing n.

Effect of disorder on phases across two-dimensional thermal melting.

We study melting in a two-dimensional system of classical particles with Gaussian-core interactions in disordered environments. The pure system validates the conventional two-step melting with a hexatic phase intervening between the solid and the liquid. This picture is modified in the presence of pinning impurities. A random distribution of pinning centers forces a hexaticlike low-temperature phase that transits into a liquid at a single melting temperature T_{m}^{RP}. In contrast, pinning centers located at randomly chosen sites of a perfect crystal anchor a solid at low temperatures which undergoes a direct transition to the liquid at T_{m}^{CP}. Thus, the two-step melting is lost in either case of disorder. We discuss the characteristics of melting depending on the nature of the impurities.

Scaling and Localization in Multipole-Conserving Diffusion.

We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are exponentially localized near system boundaries. It also yields an unusual approach to equilibrium, which in d dimensions exhibits scaling with dynamical exponent z=4+d. Similar phenomena occur for dynamics that conserves higher moments of the density, which we systematically classify using a family of nonlinear diffusion equations. In the quantum setting, analogous fermionic systems are shown to form real-space Fermi surfaces, while bosonic versions display a real-space analog of Bose-Einstein condensation.

Classical stochastic approach to quantum mechanics and quantum thermodynamics

We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component φ j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associated with a degree of freedom of the underlying classical system. From the classical stochastic equations of motion, we derive a general equation for the covariance matrix of the wave vector, which turns out to be of the Lindblad type. When the noise changes only the phase of φ j , the Schrödinger and the quantum Liouville equations are obtained. The component ψ j of the wave vector obeying the Schrödinger equation is related to the stochastic wave vector by |ψj|2=⟨|ϕj|2⟩ .

Phase-space evolution of quasiparticle excitations in electron gas

In this research, we use the dual lengthscale quasiparticle model for collective quantum excitations in electron gas to study the time evolution of the Wigner function. The linearized time-dependent Schrödinger–Poisson system for quasiparticles is used to study the dynamics of initial known stationary and damped solutions in an electron gas with arbitrary degree of degeneracy. The self-consistent potential in the Schrödinger–Poisson model is treated in a quite different manner in this analysis due to the effective coupling of the electrostatic field to the electron density, which leads to a modified Wigner function. It is shown that the modified Wigner function in the absence of external potential evolves similar to the system of free particles, a feature of collective quantum excitations which is quite analogous to freely evolving classical system of particles in the center of mass frame in the absence of external forces. The time evolution of the modified Wigner function reveals a grinding effect on large-amplitude density structures present at initial states, which is a characteristic feature of the Landau damping in plasmas. It is further shown that linear phase-space dynamics of spill-out electrons (damped quasiparticles) can be described similar to free quasiparticles with imaginary momentum. The later predicts the surface electron tunneling via the collective excitations of spill-out electrons at the half-space boundary, which is closely related to the Heisenberg's uncertainty principle. Current research can have applications in plasmonics and related fields.

On the analyticity of the pressure for a non-ideal gas with high density boundary conditions

We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.

Cuplength estimates for periodic solutions of Hamiltonian particle-field systems

We consider a natural class of time-periodic infinite-dimensional nonlinear Hamiltonian systems modelling the interaction of a classical mechanical system of particles with a scalar wave field. When the field is defined on a space torus {mathbb {T}}^d={mathbb {R}}^d/(2pi {mathbb {Z}})^d and the coordinates of the particles are constrained to a submanifold Qsubset {mathbb {T}}^d, we prove that the number of contractible T-periodic solutions of the coupled Hamiltonian particle-field system is bounded from below by the {mathbb {Z}}_2-cuplength of the space Lambda ^{{text {contr}}} Q of contractible loops in Q, provided that the square of the ratio T/2pi of time period T and space period X=2pi is a Diophantine irrational number. The latter condition is necessary since for the infinite-dimensional version of Gromov–Floer compactness as well as for the C^0-bounds we need to deal with small divisors.

Ultrasoft Classical Systems at Zero Temperature

At low temperatures, classical ultrasoft particle systems develop interesting phases via the self-assembly of particle clusters. In this study, we reach analytical expressions for the energy and the density interval of the coexistence regions for general ultrasoft pairwise potentials at zero temperatures. We use an expansion in the inverse of the number of particles per cluster for an accurate determination of the different quantities of interest. Differently from previous works, we study the ground state of such models, in two and three dimensions, considering an integer cluster occupancy number. The resulting expressions were successfully tested in the small and large density regimes for the Generalized Exponential Model α, varying the value of the exponent.

Convergence rates for energies of interacting particles whose distribution spreads out as their number increases

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global minimum of an interaction energy, which consists of a nonlocal, repulsive interaction part and a confining part. Motivated by the applications, we cover non-standard scenarios in which the confining potential weakens as the number of particles increases. This results in a large area over which the particles spread out. Our aim is to approximate the particle interaction energy by a corresponding continuum interacting energy. Our main results are bounds on the corresponding energy difference and on the difference between the related potential values. We demonstrate that these bounds are useful to problems in approximation theory and plasticity. The proof of these bounds relies on convexity assumptions on the interaction and confining potentials. It combines recent advances in the literature with a new upper bound on the minimizer of the continuum interaction energy.

Effective Hamiltonian for the system of the electromagnetic field and charged particles

A classical system of point charged particles and electromagnetic field is investigated in the general formulation, in which there is no direct interaction of the particles with each other. Particles are assumed to be non-relativistic for research simplicity. The point of view is defended that gauge choice determines the physical picture of processes in the system. The idea of extended gauge, in which scalar φk and longitudinal part Alnk of the vector potentials transform separately for large and small wave numbers, is proposed. Moreover, in the new gauge φk ≠ 0 only when k ≥ k0 and Alnk ≠ 0 only when k ≤ k0 , where k0 is a certain wave number. This greatly simplifies the study of the system dynamics, in which the transversecomponents Atnk of the vector potential are taken into account and do not change at the gauge transformation. Basing on the extended gauge idea, it is established that the system has a massive oscillatory mode described by a transverse potential Atnk and an oscillatory mod described by a longitudinal potential Alnk with the laws of dispersion (ωk2 + ω02 )1/2 і ω0, respectively (ωk = ck is the dispersion law for electromagnetic waves in vacuum, and ω0 is the plasma frequency). These modes can be called electromagnetic and plasma ones. At the same time, effective interaction between charged particles is introduced, which describes the screening effect. A connection of our work with Bohm and Pines investigations related to the presence of plasma modes in a Coulomb system, in which they do not use idea of gauge transformations, is analyzed.

Homogeneous generalized master equation for an arbitrary initial state of a many-particle classical system

A special projection operator is introduced, which exactly transforms the Nakajima–Zwanzig inhomogeneous Generalized Master Equation (GME) with an irrelevant initial condition term (a source) into a completely closed homogeneous GME (with no initial correlations term) for the relevant part of an N-particle distribution function FN(t) for an arbitrary initial distribution function FN(0) of a system of classical particles. It resolves the problem of the derivation of a closed linear evolution equation from the Liouville equation with no “molecular chaos” type approximation. The obtained equation is equivalent to the completely closed equation for s-particle (s≤N) distribution function Fs(t). The initial correlations are accounted for in this equation in the modified by the introduced projection operator kernel governing the evolution of Fs(t). This equation is further simplified by presenting its kernel in the linear in the particles’ density n approximation. In this approximation the equations for one-particle F1(t) and two-particle F2(t) distribution functions are derived. Special attention is given to analyzing the equation for F1(t) and showed that this equation in the Markov approximation can be written as the linear Boltzmann or Landau (for a small interparticle interaction) equations but with additional terms caused by initial correlations.

Holomorphic representation of quantum computations

We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser particles corresponding to the zeros of the holomorphic function, together with a conformal evolution of Gaussian parameters. We explain that the Calogero-Moser dynamics is due to unique features of bosonic Hilbert spaces such as squeezing. We then generalize the properties of this holomorphic representation to the multimode case, deriving a non-Gaussian hierarchy of quantum states and relating entanglement to factorization properties of holomorphic functions. Finally, we apply this formalism to discrete- and continuous- variable quantum measurements and obtain a classification of subuniversal models that are generalizations of Boson Sampling and Gaussian quantum computing.

State-to-State Cosmology: A New View on the Cosmological Arrow of Time and the Past Hypothesis

Cosmological boundary conditions for particles and fields are often discussed as a Cauchy problem, in which configurations and conjugate momenta are specified on an “initial” time slice. But this is not the only way to specify boundary conditions, and indeed in action-principle formulations we often specify configurations at two times and consider trajectories joining them. Here, we consider a classical system of particles interacting with short range two body interactions, with boundary conditions on the particles’ positions for an initial and a final time. For a large number of particles that are randomly arranged into a dilute gas, we find that a typical system trajectory will spontaneously collapse into a small region of space, close to the maximum density that is obtainable, before expanding out again. If generalizeable, this has important implications for the cosmological arrow of time, potentially allowing a scenario in which both boundary conditions are generic and also a low-entropy state “initial” state of the universe naturally occurs.

Investigation of the dynamic structural factor of binary ionic mixtures

The method of moments is used to investigate and analyze the dynamic characteristics of dense systems consisting of ions of two types with different masses and charges, and the number of screening electrons corresponding to the charges of the ions.In this paper, we discuss the characteristics of a binary ionic mixture whose component masses differ by a factor of two. Within the framework of the developed self-consistent method of moments, the dynamic structure factors (DSF) of such a plasma are calculated for various thermodynamic parameters. In this case, the calculation algorithm is based on the use, on the one hand, of the static structural factor of the system, which is determined from the solution of the Ornstein-Zernike equation, and on the other hand, the so-called Nevanlinna parameter function (NPF), which is included in the calculated relations. The calculations were carried out within the framework of the classical system of charged particles interacting according to the Coulomb law. The paper analyzes the data obtained using various methods for calculating the NPF. The results obtained in this work qualitatively and quantitatively agree with the data of theoretical calculations and numerical experiments of the authors of other studies of the dynamic properties of a dense multicomponent plasma.

Physics-constrained Bayesian inference of state functions in classical density-functional theory.

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: Given the experimental data on the collective motion of a classical many-body system, how does one characterize the free energy landscape of that system? By combining non-parametric Bayesian inference with physically motivated constraints, we develop an efficient learning algorithm that automates the construction of approximate free-energy functionals. In contrast to optimization-based machine learning approaches, which seek to minimize a cost function, the central idea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data are used to probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free-energy functionals, making our algorithm highly data efficient. In particular, we consider classical particle systems with excluded volume interactions, which are ubiquitous in nature, while being highly challenging in terms of free energy modeling. We validate our approach on the paradigmatic case of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher dimensional systems are conceptually straightforward, while standard coarse-graining techniques allow one to easily incorporate attractive interactions.

Classical Particles in the Continuum Subjected to High Density Boundary Conditions

We consider a continuous system of classical particles confined in a finite region \(\Lambda \) of \(\mathbb {R}^d\) interacting through a superstable and regular pair potential and subjected to non-free and non-periodic boundary conditions. We prove that the thermodynamic limit of the pressure of the system at any fixed inverse temperature \(\beta \) and any fixed fugacity \(\lambda \) does not depend on the field produced by particles outside \(\Lambda \) whose local density may increase sub-linearly with the distance from the origin at a rate that depends on how fast the pair potential decays at large distances. In particular, if the pair potential v(r) decays as \(C/r^{d+p}\) (with \(p>0\)) when the distance r approaches infinity, then the existence of the thermodynamic limit of the pressure is guaranteed in presence of boundary conditions produced by external particles which may be distributed with a local density increasing with the distance r from the origin as \(\rho (1+ r^q)\), where \(q\le {1\over 2}\min \{1, p\}\) and \(\rho \) is any positive constant (even arbitrarily larger than the mean density \(\rho _0(\beta ,\lambda )\) the system has when submitted to free boundary conditions).

Virial series for a system of classical particles interacting through a pair potential with negative minimum

In this paper, we revisit the recent and less recent developments concerning rigorous results on the Mayer series and the virial series of a continuous system of classical particles interacting via a stable and tempered pair potential and we provide new lower bounds for the convergence radius of the virial series when the potential has a strictly positive stability constant. As an application we obtain a new estimate for the convergence radius of the virial series of the Lennard-Jones gas which improves sensibly previous estimates available in the literature.

Toward a relativistic microscopic substantiation of thermodynamics: classical relativistic many-particle dynamics

An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The law of variation of the energy of a system of particles in terms of the microscopic distribution function is obtained.

Dimensionality Reduction of High Dimensional Time Series based on Artificial Neural Network

Molecular dynamics is a molecular simulation method which relies on Newtonian mechanics to simulate the motion of molecular system. In this method, some differential equations are integrated, and the results of integration are further processed to obtain the trajectory or momentum evolution process of some particles controlled by dynamic equations, and the technology of extracting the equilibrium state, motion process or related properties of classical particle system can be used. Through molecular dynamics simulation, we can obtain a series of properties of the system, which are widely used in experimental verification, theoretical derivation and other scenarios. Because it can obtain the dynamic state of macromolecules to make up for the limitations of these properties, it is widely used in the study of transmembrane proteins, polypeptide chains and other systems in life sciences. Through the kinetic path reduction of these systems, we can intuitively understand the characteristics of molecular folding, molecular motion and specific binding, which can play a very important role in the study of proteins and peptides. However, due to the characteristics of high-dimensional time series obtained by molecular dynamics simulation, it is difficult for us to pay attention to the collective state or characteristic process of the whole system in a non-equilibrium state or slow process. This is due to the difficulty in data processing and the difficulty in obtaining its characteristic function. This makes it very difficult to study the dynamic process of the whole system, especially the dynamic process at the intermediate non-equilibrium moment. It is difficult to solve this kind of problem by conventional methods, and only a few special simple systems can be solved by experience. Therefore, it is of great significance to find a method to obtain the characteristic function of the system through the trajectory obtained by molecular dynamics, and then reduce the molecular dynamics path. In order to solve this scientific problem, researchers focus on machine learning. In this study, machine learning method will be used to solve the overall non-equilibrium state of the system or the collective state of the slow process in molecular dynamics simulation. Firstly, we use this method to solve a simple one-dimensional four well model. By this method, we obtain a series of characteristic functions describing the motion process of the model. By sorting the eigenvalue contributions, we obtain some main characteristic functions describing the system. It includes the motion description of Markov smooth transition state and the motion description of four potential wells. At the same time, we use the traditional transition probability matrix to calculate. The difference between the characteristic function obtained by machine learning and the traditional method is very small, but the calculation method is simpler and more universal. After that, we apply the method to the actual scene. By solving the molecular dynamics simulation of alanine dipeptide structure in polymer protein molecule, the characteristic function of dihedral angle folding of alanine dipeptide structure was preliminarily calculated. The results were consistent with the traditional method.