The BBGKY Hierarchy and Fokker-Planck Equation for Many-Body Dissipative Randomly Driven Systems

By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton's equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the one-particle distribution function, we use a regular cut off procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases by assuming either Gaussian statistics of external perturbation or homogeneity of the system are discussed

Mechanism of collisionless sound damping in dilute Bose gas with condensate

We develop a microscopic theory of sound damping due to Landau mechanism in dilute gas with Bose condensate. It is based on the coupled evolution equations of the parameters describing the system. These equations have been derived in earlier works within a microscopic approach which employs the Peletminskii-Yatsenko reduced description method for quantum many-particle systems and Bogoliubov model for a weakly nonideal Bose gas with a separated condensate. The dispersion equations for sound oscillations were obtained by linearization of the mentioned evolution equations in the collisionless approximation. They were analyzed both analytically and numerically. The expressions for sound speed and decrement rate were obtained in high and low temperature limiting cases. We have shown that at low temperature the dependence of the obtained quantities on temperature significantly differs from those obtained by other authors in the semi-phenomenological approaches. Possible effects connected with non-analytic temperature dependence of dispersion characteristics of the system were also indicated

Propagation of relativistic charged particles in ultracold atomic gases with Bose-Einstein condensates

We study theoretically some effects produced by a propagation of the charged particles in dilute gases of alkali-metal atoms in the state with Bose-Einstein condensates. The energy change of the high-speed (relativistic) particle that corresponds to the Cherenkov effect in the condensate is investigated. We show that in the studied cases the particle can both loose and receive the energy from a gas. We find the necessary conditions for the particle acceleration in the multi-component condensate. It is shown that the Cherenkov effect in Bose-Einstein condensates can be used also for defining the spectral characteristics of atoms.Comment: 6 pages, 3 figure

Green-function method in the theory of ultraslow electromagnetic waves in an ideal gas with Bose-Einstein condensates

We propose a microscopic approach describing the interaction of an ideal gas of hydrogenlike atoms with a weak electromagnetic field. This approach is based on the Green-function formalism and an approximate formulation of the method of second quantization for quantum many-particle systems in the presence of bound states of particles. The dependencies of the propagation velocity and damping rate of electromagnetic pulses on the microscopic characteristics of the system are studied for a gas of hydrogenlike atoms. For a Bose-Einstein condensate of alkali-metal atoms we find the conditions when the electromagnetic waves of both the optical and microwave regions are slowed. In the framework of the proposed approach, the influence of an external homogeneous and static magnetic field on the slowing phenomenon is studied.Comment: 15 pages, 6 figure

Національна доповідь про стан і перспективи розвитку освіти в Україні: монографія (До 30-річчя незалежності України)

The publication provides a comprehensive analysis of the state and development of national education over the 30 years of Ukraine’s independence, identifies current problems in education, ascertains the causes of their emergence, offers scientifically reasoned ways to modernise domestic education in the context of globalisation, European integration, innovative development, and national self-identification. Designed for legislators, state officials, education institutions leaders, teaching and academic staff, the general public, all those who seek to increase the competitiveness of Ukrainian education in the context of civilisation changes.У виданні здійснено всебічний аналіз стану і розвитку національної освіти за 30-річний період незалежності України, визначено актуальні проблеми освітньої сфери, виявлено причини їх виникнення, запропоновано науково обґрунтовані шляхи модернізації вітчизняної освіти в умовах глобалізації, європейської інтеграції, інноваційного розвитку та національної самоідентифікації. Розраховано на законодавців, державних управлінців, керівників закладів освіти, педагогічних і науково-педагогічних працівників, широку громадськість, усіх, хто прагне підвищення конкурентоспроможності української освіти в контексті цивілізаційних змін

Bose-Einstein condensation of photons in an ideal atomic gas

We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine solutions of these equations in the case of high temperatures, when the atomic components of the system can be considered as nondegenerated ideal gases of atoms, and the photonic component can form a state with the Bose condensate. Transcendental equation for transition temperature and expression for the density of condensed photons in the considered system are derived. We also obtain analytical solutions of the equation for the critical temperature in a number of particular cases. The existence of two regimes of Bose condensation of photons, which differ significantly in nature of transition temperature dependence on the total density of photons pumped into the system, is revealed. In one case, this dependence is a traditional fractional-power law, and in another one it is the logarithmic law. Applying numerical methods, we determine boundaries of existence and implementation conditions for different regimes of condensation depending on the physical parameters of the system under study. We also show that for a large range of physical systems that are in equilibrium with photons (from ultracold gases of alkali metals to certain types of ideal plasma), the condensation of photons should occur according to the logarithmic regime