Exact c-number Representation of Non-Markovian Quantum Dissipation

Abstract

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr{ö}dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born--Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.