Quantum kinetic equation for electrons in metals

Abstract

A quantum kinetic equation for electrons in metal in a uniform electric field is derived by means of the Keldysh diagrammatic technique. The principle of detailed balance for the quantum collision integral is formulated. Using this concept the analogue of the single-particle distribution function, which depends on the electron 4-momentum, is defined. The linear response of an electron system to the electric field is not completely determined by the nonequilibrium part of this function. To give a complete description of the nonequilibrium state it is necessary also to know the nonequilibrium correction to the electron spectral function. An inhomogeneous integral equation for this correction is obtained, in which the inhomogeneous term is defined via the solution of the kinetic equation. This equation, supplementary to the kinetic one, is solved in the general case by the methods of the Landau theory of the Fermi liquid. While calculating the resistivity, account is taken of the spectral response results in the change of the bare electron mass by the 'Coulomb' effective mass. The electron-phonon contribution to this effective mass is as small as theta epsilon F.