Abstract:
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.