Non-Markovian Quantum State Diffusion for Spin Environments

Abstract

We introduce a theory of non-Markovian quantum state diffusion (NMQSD) for quantum systems coupled to a class of non-Gaussian environments consisting of spins. This allows us to express the time evolved reduced state of the system as the average of an ensemble of stochastically evolving pure states. We develop the theory for arbitrary linear spin environments at zero and also at finite temperature. Moreover, we introduce a hierarchical expansion which constitutes a method to numerically compute the time evolution of the stochastic pure states, and thus to solve the open system problem.