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Journal of Mathematical Physics

Master equations in quantum stochastic processes

Etang Chen

Published Oct 1, 1975• 3 citations
Publisher

Abstract

Pauli master equation is derived rigorously in the framework of quantum stochastic processes.
DOI
10.1063/1.522439

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We discuss the derivation of the Pauli master equation, based on a repeated random phase assumption, and of van Hove's result, based on an initial random phase assumption. For the former we indicate a derivation which is closer to the general approach of stochastic theory than Pauli's original method. For the van Hove result, we show that the diagonal and nondiagonal parts of the evolution operator of the Schrödinger or von Neumann equation are readily obtained by Zwanzig's projection operator method.
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov processes which are based upon the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.
In the presence of quantum measurements with direct photon detection, the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as an approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov processes, which are based on the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.