Sokolovsky S. Kinetics of electrons and phonons of a solid taking into account relaxation degrees of freedom

The work is based on the Bogolyubov reduced description method which is applied to the quantum Liouville equation and kinetic equations. Electron-phonon processes in polar crystals (in dielectrics and semiconductors) and phonon processes in dielectrics are investigated. The consideration is based on the functional hypothesis. The Chapman-Enskog method has been generalized for the case of presence of relaxation processes at their end and spatial non-locality of collision integral. Approach to construction of kinetics of completely described system in equilibrium and nonequilibrium medium has been proposed. Role of the stochastic method in construction of the reduced description taking into account nonequilibrium fluctuations (correlations) is shown. On this base: kinetic equation for strong non-uniform states of polarons in the case of quasi-equilibrium states of the phonon subsystem and in the presence of strong electric field is obtained; hydrodynamic equations for low density polaron gas in polar crystals are derived taking into account relaxation and dissipative processes and strong non-uniformity of states of the system; hydrodynamic equations for phonon subsystem of dielectrics with account for relaxation and dissipative processes are built. It is established that in the presence of relaxation processes local equilibrium assumption is not valid but in phonon hydrodynamics at low temperatures one can neglect by this phenomenon. It was shown that relaxation processes change expressions for kinetic coefficients of the system. A special role of the Umklapp processes in steady states of the system has been investigated. On the basis of stochastic method binary correlations as a new reduced description parameters are taken into account in polaron kinetics in hydrodynamic phonon medium. A number of equations which the Chapman-Enskog method gives were approximately solved by expansion in orthogonal polynomials.