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Existence, uniqueness and approximation of a stochastic Schrödinger equation: The diffusive case. (English) Zbl 1167.60006

Stochastic Schödinger equations, or Belavkin equations, are perturbations of Schrödinger type equations. They describe the evolution of an open quantum system undergoing a continuous quantum measurement which is at the origin of the stochastic character of the evolution. Existence and uniqueness are proven for the solution of these equations in the diffusive case with a two-level system. Then the model is physically justified by proving that it is a continuous time limit of a discrete physical procedure with repeated quantum interactions.

MSC:

60F05 Central limit and other weak theorems
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60J60 Diffusion processes
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