Why and how to avoid standard kinetic equations II. Time-convolution or convolutionless equations and hopping

Abstract

Review of ideas questioning applicability of standard approximate kinetic equations derived from Generalized Master Equations (GME) with time-independent projector, in particular in the long-time (low-frequency) domain except for special situations, is given. Attention is concentrated on the time-convolutionless GME for systems interacting with a reservoir with applications to the phonon-assisted hopping problem. As compared to the previous work of the series, the treatment is extended to any power of the external field. Inapplicability of mathematical methods justifying standard markovian treatments in the Van Hove limit is found to be owing to finite coupling constants encountered in nature. It is argued that performing (for finite coupling constants usually necessary) approximations in a consistent way (preserving some exact identities derived here) means, in fact, avoiding the approximate kinetic equation method. The existence of an alternative stemming from GME is argued.