Quantum Stochastic Differential Equation

Details Quantum Stochastic Differential Equation Quantum Stochastic Differential Equation

2005-12-22

arxiv.org/abs/math-ph/0512078v1

J. Math. Phys. 41 No 11, 2000, 7220--7233

Physics

Mathematical Physics

17 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/evo_equ.html and http://www.maths.not

Scientific paper

10.1063/1.1310357

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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