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Quantum Stochastic Differential Equation

V. P. Belavkin·P. Staszewski
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Abstract

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a contraction C. The counting trajectories are assumed to satisfy the Poisson law. A unitary dilation of the concractive stochastic dynamics is found. In particular, in the limit of frequent detection corresponding to the large number limit we obtain the Ito-Schroedinger stochastic unitary evolution for the pure state of unstable quantum system providing a new stochastic version of the quantum Zeno effect.

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V. P. Belavkin, P. Staszewski. 2005-12-22. Quantum Stochastic Differential Equation. https://doi.org/10.1063/1.1310357

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