Phase Space Localization and Approach to Thermal Equilibrium for a Class of Open Systems

Abstract

We analyse the evolution of a quantum oscillator in a finite temperature environment using the quantum state diffusion (QSD) picture. Following a treatment similar to that of reference [7] we identify stationary solutions of the corresponding It\^o equation. We prove their global stability and compute typical time scales characterizing the localization process. The recovery of the density matrix in approximately diagonal form enables us to verify the approach to thermal equilibrium in the long time limit and we comment on the connection between QSD and the decoherent histories approach.