Stochastic Master Equations in Thermal Environment

We derive stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. It is well-known that at zero temperature one obtains stochastic differential equations of jump-diffusion type. We show that only pure diffusion type equations are relevant at strictly positive temperatures.

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