Solution of the kinetic equation for thin two-and three-dimensional metallic slabs with diffuse boundary scattering and arbitrary impurity scattering in the bulk

The integrodifferential equation in the phase space, describing the response to a homogeneous electric field of a two- or three-dimensional isotropic metallic slab with diffuse scattering on the border and arbitrary scattering of impurities, is transformed into the system of inhomogeneous integral equations in the configuration space. It is shown that one of the functions fulfilling this system is simply connected with the current response of the slab. The general solution of this system is found in the form of asymptotical expansion provided that the mean-free path is much greater than the width of the slab. In the opposite limit, the asymptotic solution is found only at almost isotropic impurity scattering. In other words, the Fuchs problem (1938) has been solved for thin slabs at a real low-temperature collision integral. 14 ref.--AA