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.