The Kramers problem for quantum bose-gases with constant collision frequency and specular-diffusive boundary conditions

TL;DR

This paper develops a new generalized method based on source representation and Fourier integrals to solve the Kramers problem for quantum Bose-gases with boundary conditions, achieving arbitrary accuracy.

Contribution

A novel generalized method for solving boundary problems in quantum Bose-gases using source representation and integral equations, allowing arbitrary accuracy.

Findings

Method yields solutions with any desired accuracy.

Reduces kinetic equations to Fredholm integral equations.

Uses Neumann series for solution expansion.

Abstract

The Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers' problem the new generalized method of a source of the decision of the boundary problems from the kinetic theory is developed. The method allows to receive the decision with any degree of accuracy. At the basis of a method lays the idea of representation of a boundary condition on distribution function in the form of a source in the kinetic equation. By means of integrals Fourier the kinetic equation with a source is reduced to the integral equation of Fredholm type of the second kind. The decision is received in the form of Neumann's series.