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Numerical solution of stochastic quantum master equations using stochastic interacting wave functions. (English) Zbl 1415.82014

Summary: We develop a new approach for solving stochastic quantum master equations with mixed initial states. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of Schrödinger type. Then, we design three exponential schemes for these coupled stochastic Schrödinger equations, which are driven by Brownian motions and jump processes. Hence, we have constructed efficient numerical methods for the stochastic master equations based on quantum trajectories. The good performance of the new numerical integrators is illustrated by simulations of two quantum measurement processes.

MSC:

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
81S22 Open systems, reduced dynamics, master equations, decoherence
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics

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