Viatcheslav Belyi

A generalization of the Balescu-Lenard equation and the pair correlation function for a weakly non-ideal plasma

Taking into account the first non-Markovian correction to the Balescu–Lenard equation, we derive an expression for the pair correlation function and a nonlinear kinetic equation valid for a weakly non-ideal polarized classical plasma. This equation allows for the description of the correlational energy evolution and exhibits global conservation of energy with dynamical polarization.

Kinetic theory of a weakly-nonideal spatially nonuniform polarizable plasma

A nonmarkovian and nonlocal kinetic equation, which is a generalization of the (nonlinear) Balescu-Lenard equation, is derived for a weakly nonuniform multicomponent polarizable plasma. A specific expansion of the plasma resolvent, which allows to separate the dymamic, kinetic and hydrodynamic scales, is proposed. Explicit expressions of the collision integral and of the nonequilibrium pair correlation function are given in an approximation which takes into account the effects of spatial and temporal nonlocality as well as of the polarization. Balance equations for the momentum and energy densities are calculated in the first order in nonlocality, and potential contributions to the fluxes due to polarization are obtained.

Fluctuations out of equilibrium

A generalization of the fluctuation‐dissipation formula for systems with slowly varying parameters is given using the Langevin approach and momentum method. It is shown that spectral function of the fluctuations in these systems is determined not only by the dissipation but also by the derivations of the dispersion. The non Joule dispersion contribution is characterized by a new nonlocal effect originating from an additional phase shift between the force and response of the system. That phase shift results from the parametric control to the system.

Bogolyubov kinetic equations and dielectric function with exchange interaction

Starting with the quantum BBGKY-hierarchy for the statistical operators, we have obtained the quantum kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma.

Non Equilibrium Fluctuations In The Degenerated Polarizable Plasma

The quantum plasma of Bose and Fermi particles is considered. A scheme of equation linearization for density matrix with the exchange interaction taken in account is proposed and the equation solution is found. An expression for Hartree‐ Fock dielectric permittivity with the exchange interaction is obtained. This interaction is taken into account in the exchange scattering amplitude. With the use of obtained solutions the non‐equilibrium spectral function of electric field fluctuations in presence of exchange interaction and medium polarization is found. It is shown that in the state of thermodynamic equilibrium a Fluctuation‐Dissipation Theorem holds. An expression for the system’s response to an external electric field in presence of exchange interaction is given.

The Balescu kinetic equation with exchange interaction

Starting with the quantum BBGKY-hierarchy for the distribution functions, we have obtained the quantum kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma. The collision integral is expressed in terms of the Green function of the linearized Hartree-Fock equation.The potential energy takes into account the polarization and exchange interaction too.

On the model kinetic description of plasma and a boltzmann gas of hard spheres

A new form of the collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is proposed. One-component and many-component systems are considered. The proposed collision operator properly takes into account the relaxation of the first 13 hydrodynamic moments. Besides this, it accounts for the non-diagonal component contribution in the quadratic approximation in the expansion of the linearized collision operator with respect to the complete system of Hermite polynomials. It is shown that for a system of charged particles with the Coulomb interaction potential, these contributions are essential and lead to Spitzer corrections to the transport coefficients. An expression for the intensity of the Langevin source in the kinetic equation is obtained in the same approximation. A new form of the model collision operator for a Boltzmann gas of hard spheres is proposed. For a many-component system we have reconstructed a non-linear model collision integral by using the linearized collision integral found. Unlike previous ones, it does not contain complicated exponential dependence and avoids coefficient ambiguity in the many-component collision integral.

Pair correlation function for plasma with polarization and exchange interaction

Starting with the quantum BBGKY-hierarchy for the distribution functions, we have solved the equation for the quantum pair correlation function with the non-Markovian correction, the polarization and the exchange interaction included. The solution is expressed in terms of the Green function of the linearized Hartree - Fock equation. The quantum non - Markovian kinetic equation obtained includes the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma.

Fluctuation‐Dissipation Dispersion Relation for Systems with Slowly Varying Parameters

A generalization of the fluctuation‐dissipation formula for systems with slowly varying parameters is given using the Langevin approach and momentum method. It is shown that spectral function of the fluctuations in these systems is determined not only by the dissipation but also by the derivations of the dispersion. The non Joule dispersion contribution is characterized by a new nonlocal effect originating from an additional phase shift between the force and response of the system. That phase shift results from the parametric control to the system. The general formalism is illustrated for an oscillating electrical circuit. It is shown that in that systems the dispersive contributions strongly affect the quality factor.