Stochastic evolution in quantum systems
Stig Stenholm · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · 1996
Starting from the standard Lindblad form of a dissipative master equation, we identify a stochastic parameter in the quantum time evolution. This lacks dynamic evolution but its value is affected by the dissipative part of the master equation. An unravelling of the master equation in terms of quantum trajectories then shows this parameter performing the erratic variation characteristic of a stochastic variable. When the two evolutions separate, the stochastic Markov process can be extracted and solved independently and imposed on the parameter of the quantum evolution. This is the traditional form of treatment of stochastic variables in quantum mechanics. The relations to earlier works are established, and the approach is illustrated by simple model examples.