476 research outputs found
Anomalous Diffusion in Velocity Space
The problem of anomalous diffusion in the momentum space is considered on the
basis of the appropriate probability transition function (PTF). New general
equation for description of the diffusion of heavy particles in the gas of the
light particles is formulated on basis of the new approach similar to one in
coordinate space (S. Trigger et al.). The obtained results permit to describe
the various situations when the probability transition function (PTF) has a
long tail in the momentum space. The effective friction and diffusion
coefficients are found.Comment: 11 pages, no figures and table
Non-Planck equilibrium radiation in plasma model of early Universe
Consideration of the adiabatic character of radiation expansion in early
Universe leads to the conclusion that equilibrium distribution of the
primordial radiation in the presence of charged particles could be different
from the Planck distribution in some regions of the spectrum. The equilibrium
distribution of electromagnetic radiation (the black body radiation) is
generalized for the system containing an extremely dense fully ionized plasma.
The conditions of the adiabatic expansion of radiation for the model of the
early Universe are found.Comment: 10 pages, 4 figure
Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems
A self-consistent and universal description of friction and diffusion for
Brownian particles (grains) in different systems, as a gas with Boltzmann
collisions, dusty plasma with ion absorption by grains, and for active
particles (e.g., cells in biological systems) is suggested on the basis of the
appropriate Fokker-Planck equation. Restrictions for application of the
Fokker-Planck equation to the problem of velocity-dependent friction and
diffusion coefficients are found. General description for this coefficient is
formulated on the basis of master equation. Relation of the diffusion
coefficient in the coordinate and velocity spaces is found for active (capable
to transfer momentum to the ambient media) and passive particles in the
framework of the Fokker-Planck equation.
The problem of anomalous space diffusion is formulated on the basis of the
appropriate probability transition (PT) function. The method of partial
differentiation is avoided to construct the correct probability distributions
for arbitrary distances, what is important for applications to different
stochastic problems. Generale equation for time-dependent PT function is
formulated and discussed.
Generalized friction in the velocity space is determined and applied to
describe the friction force itself as well as the drag force in the case of a
non-zero driven ion velocity in plasmas. The negative friction due to ion
scattering on grains exists and can be realized for the appropriate
experimental conditions.Comment: 21 page
Anomalous Transport in Velocity Space: Equation and Models
The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). A new general equation for the description of the diffusion of heavy particles in a gas of light particles is formulated on the basis of the new approach similar to one in the coordinate space. The obtained results allow one to describe the various situations where the probability transition function has a long tail in the momentum space. The effective friction and diffusion coefficients are determined.Проблему аномальної дифузiї в iмпульсному просторi розглянуто на основi вiдповiдної функцiї iмовiрностi переходiв. Нове загальне рiвняння для опису дифузiї важких частинок у газi легких частинок одержано на основi нового наближення, яке використано автором ранiше для дифузiї в координатному просторi. Одержанi результати дозволяють описати рiзнi ситуацiї, коли функцiя iмовiрностi переходiв має довгий хвiст у iмпульсному просторi. Одержано ефективнi коефiцiєнти тертя та дифузiї
Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer probability approach
Fokker-Planck equation with the velocity-dependent coefficients is considered
for various isotropic systems on the basis of probability transition (PT)
approach. This method provides the self-consistent and universal description of
friction and diffusion for Brownian particles. Renormalization of the friction
coefficient is shown to occur for two dimensional (2-D) and three dimensional
(3-D) cases, due to the tensorial character of diffusion. The specific forms of
PT are calculated for the Boltzmann-type of collisions and for the
absorption-type of collisions (the later are typical for dusty plasmas and some
other systems). Validity of the Einstein's relation for the Boltzmann-type
collisions is analyzed for the velocity-dependent friction and diffusion
coefficients. For the Boltzmann-type collisions in the region of very high
grain velocity as well as it is always for non-Boltzmann collisions, such as,
e.g., absorption collisions, the Einstein relation is violated, although some
other relations (determined by the structure of PT) can exist. The generalized
friction force is investigated in dusty plasma in the framework of the PT
approach. The relation between this force, negative collecting friction force
and scattering and collecting drag forces is established.+AFwAXA- The concept
of probability transition is used to describe motion of active particles in an
ambient medium. On basis of the physical arguments the PT for a simple model of
the active particle is constructed and the coefficients of the relevant
Fokker-Planck equation are found. The stationary solution of this equation is
typical for the simplest self-organized molecular machines.+AFwAXA- PACS
number(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-yComment: 18 page
Electromagnetic field energy and radiation intensity in a medium with temporal and spatial dispersion outside the transparency domain
Calculation of electromagnetic field energy in a medium with temporal and spatial dispersion outside the
transparency domain is discussed. It is shown that charged particle contribution to the energy of electromagnetic
perturbations in the general case can be described in terms of a bilinear combination of the dielectric polarizability
of the medium. The explicit form of such contribution is found. The relations obtained are used to generalize the
Planck law and Kirchhoff law to the case of an absorptive medium with spatial dispersion.Розраховано енергію електромагнітного поля в середовищі з часовою та просторовою дисперсіями поза
областю прозорості. Показано, що в загальному випадку внесок енергії частинок середовища в енергію
електромагнітного збурення описується в термінах білінійних комбінацій діелектричної поляризованості
середовища. Знайдено явний вигляд такого внеску. Отримані результати використано для узагальнення закону
Планка і закону Кірхгофа для поглинального середовища з просторовою дисперсією.Рассчитаны энергии электромагнитного поля в среде с временной и пространственной дисперсиями вне
области прозрачности. Показано, что в общем случае вклад энергии частиц среды в энергию электромагнитного
возмущения описывается в терминах билинейных комбинаций диэлектрической поляризуемости среды. Найден
явный вид такого вклада. Полученные результаты использованы для обобщения закона Планка и закона
Кирхгофа для поглощающей среды с пространственной дисперсией
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").Comment: 8 pages, no figure
Remarks on the Nyquist and Callen-Welton Theorems
The connection of the Callen-Welton and Nyquist fluctuation-dissipation
relations is considered for plasma-like classical and quantum systems. The
conditions for appearance of the dissipative parameters in the equilibrium
current-current correlation function are investigated. The paper presents the
arguments for the restrictions of the Nyquist theorem and against violation of
the Callen-Welton theorem in the quantum case.Comment: 14 pages, 0 figures, sumitted in Physica
Rotational kinetics of absorbing dust grains in neutral gas
We study the rotational and translational kinetics of massive particulates
(dust grains) absorbing the ambient gas. Equations for microscopic phase
densities are deduced resulting in the Fokker-Planck equation for the dust
component. It is shown that although there is no stationary distribution, the
translational and rotational temperatures of dust tend to certain values, which
differ from the temperature of the ambient gas. The influence of the inner
structure of grains on rotational kinetics is also discussed.Comment: REVTEX4, 20 pages, 2 figure
A measurement of the tau mass and the first CPT test with tau leptons
We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV
using tau pairs from Z0 decays. To test CPT invariance we compare the masses of
the positively and negatively charged tau leptons. The relative mass difference
is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.
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