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S. A. Trigger

Publications and source records attributed to S. A. Trigger.

At least 37 records · Page 2Linked to original sources
arXiv2011

Advances in the studies of anomalous diffusion in velocity space

A generalized Fokker-Planck equation is derived to describe particle kinetics in specific situations when the probability transition function (PTF) has a long tail in momentum space. The equation is valid for an arbitrary value of the transferred in a collision act momentum and for the arbitrary mass ratio of the interacting particles. On the basis of the generalized Fokker-Planck equation anomalous diffusion in velocity space is considered for hard sphere model of particle interactions, Coulomb collisions and interactions typical for dusty plasmas. The example of dusty plasma interaction is peculiar in way that it leads to a new term in the obtained Fokker-Planck-iike equation due to the dependence of the differential cross-section on the relative velocity. The theory is also applied to diffusion of heavy particles in the ambience of light particles with a prescribed power-type velocity distribution function. In general, the theory is applicable to consideration of anomalous diffusion in velocity space if the typical velocity of one sort of particles undergoing diffusion is small compared to the typical velocity of the background particles.

cond-mat.stat-mech↗
arXiv2011

Exact Density Functional for the Non-Relativistic Particle Energy in the Local External Field

Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that, when considering more than two noninteracting electrons, the energy of such a system cannot be an inhomogeneous density functional. This means that the Hohenberg-Kohn lemma which assert that in the ground state to each inhomogeneous density corresponds only one potential of the external field cannot be a justification of the existence of the universal density functional in the general case. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect.

cond-mat.stat-mech↗
arXiv2010

Identity of electrons and ionization equilibrium

It is perhaps appropriate that, in a year marking the 90th anniversary of Meghnad Saha seminal paper (1920), new developments should call fresh attention to the problem of ionization equilibrium in gases. Ionization equilibrium is considered in the simplest "physical" model for an electronic subsystem of matter in a rarefied state, consisting of one localized electronic state in each nucleus and delocalized electronic states considered as free ones. It is shown that, despite the qualitative agreement, there is a significant quantitative difference from the results of applying the Saha formula to the degree of ionization. This is caused by the fact that the Saha formula corresponds to the "chemical" model of matter.

cond-mat.stat-mech↗
arXiv2010

On the Necessary Conditions for the Validity of the Hohenberg-Kohn Theorem

It is shown that the Hohenberg-Kohn lemma and theorem are direct consequences of the statement that the ground state energy (or free energy) of a system of interacting particles in an external field is a unique functional of the potential of this field. This means that, if the Hohenberg-Kohn theorem is valid, the nonuniform density in the equilibrium system and the external field potential are biunique functionals. In this case, the nonuniform density is intimately related to the inverse response function. On this basis, a regular procedure can be constructed for determining the density functional for the free energy or ground state energy.

cond-mat.stat-mech↗
arXiv2010

Exact limiting relation between the structure factors in neutron and x-ray scattering

The ratio of the static matter structure factor measured in experiments on coherent X-ray scattering to the static structure factor measured in experiments on neutron scattering is considered. It is shown theoretically that this ratio in the long-wavelength limit is equal to the nucleus charge at arbitrary thermodynamic parameters of a pure substance (the system of nuclei and electrons, where interaction between particles is pure Coulomb) in a disordered equilibrium state. This result is the exact relation of the quantum statistical mechanics. The experimental verification of this relation can be done in the long wavelength X-ray and neutron experiments.

cond-mat.stat-mech↗
arXiv2010

Finite Size Atom in the Hartree-Fock Approximation: New Substance Quasiparticle

It is shown that, in the self-consistent quantum statistical Hartree-Fock approximation, the number of electronic states localized on one nucleus is finite. This result is obtained on the basis of the general electron-nuclear model of matter and provides convergence of the atomic statistical sum and finiteness of the "atom" size. In general approach the characteristic size of the "atom" is a function of density and temperature. However, it is shown, that in a wide range of thermodynamic parameters, for relatively low temperatures, characteristic orbits and electron energy eigenvalues are independent of density and temperature. In this case, the sizes of the orbits are of order of the Bohr radius which is a minimal characteristic size in the system for typical parameters of plasma with atomic states.

cond-mat.stat-mech↗
arXiv2010

Quantum nature of the critical points of substances

Thermodynamics of chemical elements, based on the two-component electron-nuclear plasma model shows that the critical parameters for the liquid-vapor transition are the quantum values for which the classical limit is absent.

cond-mat.stat-mech↗
arXiv2010

Diffusion in a Time-dependent External Field

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as a function of instantaneous displacements. The more complicated case of long tails in the PTD will be discussed separately. We also discuss diffusion on the basis of hydrodynamic and kinetic equations and show the validity of the phenomenological approach. A new type of "collision" integral is introduced for the description of diffusion in a system of particles, which can transfer from a moving state to the rest state (with some waiting time distribution). The solution of the appropriate kinetic equation in the external field also confirms the phenomenological approach of the generalized master equation.

cond-mat.stat-mech↗
arXiv2010

Density functional theory and free energy of inhomogeneous electron gas

It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn theorem is proved in the canonical ensemble for inhomogeneous electron gas at finite temperature. The principal difference between consideration in the framework of quantum statistics in the canonical ensemble and quantum-mechanical consideration of a finite number of particles in infinite volume is established. The problem of universality of the density functional for describing the inhomogeneous electron density in a disordered nuclei field is considered.

cond-mat.stat-mech↗
arXiv2010

Anomalous Transport in Velocity Space, from Fokker-Planck to General Equation

The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is applied with necessary modifications to velocity space. A new general equation for the time evolution of the momentum distribution function in momentum space is derived. This allows the solution of various problems of anomalous transport when the probability transition function (PTF) has a long tail in momentum space. For the opposite cases of the PTF rapidly decreasing as a function of transfer momenta (when large transfer momenta are strongly suppressed), the developed approach allows us to consider strongly non-equilibrium cases of the system evolution. The stationary and non-stationary solutions are studied. As an example, the particular case of the Boltzmann-type PT-function for collisions of heavy and light particles with the determined (prescribed) distribution function, which can be strongly non-equilibrium, is considered within the proposed general approach. The appropriate diffusion and friction coefficients are found. The Einstein relation between the friction and diffusion coefficients is shown to be violated in these cases.

cond-mat.stat-mech↗
arXiv2010

Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems

The mutual influence of singularities of the dielectric permittivity e(q,w) in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and opposite q tends to zero, w tends to zero is established. It is shown that the dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which possesses the singularity due to a finite value of the static conductivity. This singularity is associated with the long "tails" of the time correlation functions.

cond-mat.stat-mech↗
arXiv2010

On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.

cond-mat.stat-mech↗
arXiv2009

True Dielectric and Ideal Conductor in Theory of the Dielectric Function for Coulomb System

On the basis of the exact relations the general formula for the static dielectric permittivity e(q,0) for Coulomb system is found in the region of small wave vectors q. The obtained formuladescribes the dielectric function e(q,0) of the Coulomb system in both states in the "metallic" state and in the "dielectric" one. The parameter which determines possible states of the Coulomb system - from the "true" dielectric till the "ideal" conductor is found. The exact relation for the pair correlation function for two-component system of electrons and nuclei g_ei(r) is found for the arbitrary thermodynamic parameters.

cond-mat.stat-mech↗
arXiv2009

Theory of degenerate Bose gas without anomalous averages

Theory of a weakly non-ideal Bose gas in the canonical ensemble is developed without assumption of the C-number representation of the creation and annihilation operators with zero momentum. It is shown that the pole of the "density-density" Green function exactly coincides with the Bogolybov's phonon-roton spectrum of excitations. At the same time in the one-particle excitation spectrum a gap exists. The value of this gap is connected with the density of particles in the "condensate".

cond-mat.quant-gas↗
arXiv2009

Coexistence of the "bogolons" and the one-particle spectrum of excitations with a gap in the degenerated Bose gas

Properties of the weakly non-ideal Bose gas are considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function of the degenerated Bose gas are calculated on the basis of the self-consistent Hartree-Fock approximation. It is shown that the spectrum of the one-particle excitations possesses a gap whose value is connected with the density of particles in the "condensate". At the same time, the pole in the "density-density" Green function determines the phonon-roton spectrum of excitations which exactly coincides with one discovered by Bogolyubov for the collective excitations (the "bogolons").

cond-mat.quant-gas↗
arXiv2009

On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit

On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in both limits: in the "metallic" state and in the "dielectric" one. On this basis the determinations of the "apparent" dielectric and the "apparent" radius of screening are introduced. In the random phase approximation (RPA) the exact relations for the function dielectric function of the electron gas in the long-wavelength region of the wave vectors are found for an arbitrary degeneration of the particles.

cond-mat.stat-mech↗
arXiv2009

Collective excitations and the gap in spectrum of the degenerated Bose gas

Model of the degenerated weakly non-ideal Bose gas is considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function are calculated on basis of the suggestion about C-number representation of the operator of particle density in the Bose condensate. It is shown, that the pole in the "density-density" Green function determines the Bogolyubov's spectrum of the collective excitations, which have the phonon-roton form. At the same time the spectrum of the one-particle excitations possesses a gap, whose value is connected with the density of particles in the Bose condensate.

cond-mat.quant-gas↗