Non-Markovian quantum state diffusion: Perturbation approach

Details Non-Markovian quantum state diffusion: Perturbation approach Non-Markovian quantum state diffusion: Perturbation approach

1999-02-10

arxiv.org/abs/quant-ph/9902043v1

Phys.Rev. A60 (1999) 91-103

Physics

Quantum Physics

23 pages, 4 figures

Scientific paper

10.1103/PhysRevA.60.91

We present a perturbation theory for non-Markovian quantum state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Physical Review {\bf A 58}, 1699, (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general non-Markovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.

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