Memory Function Methods for Quantum Systems in Contact with Reservoirs

Abstract

In recent years increasing use has been made of methods of quantum statistics and stochastic processes in a variety of problems in quantum optics. A comprehensive list of references can be found in the review articles of Agarwal [1] and Haken [2], see also a recent work of Gronchi and Lugiato [3]. In many cases of practical interest one is concerned with the dynamics of an open systems S moving irreversibly under the influence of a reservoir R. Ultimately, the properties of S are inferred through the elimination of the R-variables. This is usually accomplished by two complementary approaches: (i) The elimination procedure in the Schrodinger picture leads to an equation for a reduced density operator (master equation). (ii) The elimination procedure in the Heisenberg picture leads to a generalized, including memory effects, Langevin equation.