Quantum Stochastic Differential Equation
摘要
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.
引用
@article{arxiv.math-ph/0512078,
title = {Quantum Stochastic Differential Equation},
author = {V. P. Belavkin and P. Staszewski},
journal= {arXiv preprint arXiv:math-ph/0512078},
year = {2009}
}
备注
17 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/evo_equ.html and http://www.maths.nott.ac.uk/personal/vpb/research/mar_dyn.html