On the expansion of linear response functions?Application to electrical conductivity of disordered metals

Abstract

Two expansions for linear response functions which are based on different time-ordering prescriptions are presented. The expansions are associated with the derivation of reduced equations of motion (REM) which are nonlocal and local in time, respectively. Both expansions are formally exact and are written in a closed form but they may yield very different results once approximations are made. Therefore they are expected to be useful for different statistical properties of the system. The time-local expansion has certain formal advantages over the nonlocal one, which makes it applicable to a wide class of problems. In the weak-coupling Markovian limit the two expansions are identical. Application is made to disordered metals where explicit expressions are derived for the electrical conductivity using both reduction schemes.