The use of time-dependent projection operators in the derivation of master equations

Abstract

In this paper we generalize our previous work on the use of time-dependent projection operators for the derivation of master equations for general systems. Previously we had generalized the usual time-independent projection operator approach to include time-dependent projection operators, in which the “relevant” part of the full density operator is considered to be the uncorrelated part of the full density operator. The “irrelevant” part of the density operator was then the part describing the correlations between the coupled systems. In the present work we present new time-dependent projections operators which have the property that some correlations between the interacting subsystems are placed in the “relevant” part of the distribution function and the remaining correlations are placed in the “irrelevant” part of the distribution function.