Relaxation of electrons on impurities in super conductors

In the method of kinetic equations with self-consistent field for the generalized electron density matrix of superconductor, the time evolution of density matrix is studied, taking into account the scattering of electrons on impurities, in the case when the ratio of the mean free path to the correlation radius of superconducting electrons is arbitrary. To this end the equations for real electron propagation functions (retarded and advanced) in general non-stationary and spatially inhomogeneous case are constructed with the aid of multiple scattering theory and the separation of the “coherent” and “non-coherent” contributions vanishing after averaging over impurities coordinates is performed. Character of asymptotic states is analysed, which arise on the first stage of the evolution (before the relaxation with respect to energy), when the characteristic “frequency” representation (64) of the density matrix with arbitrary non-equilibrium distribution function over frequencies is established (the distribution function being the analogue of the classical distribution function over energy). Kinetic equations for this function are constructed, describing slow relaxation to the thermodynamical equilibrium state.