Time-Local Master Equations: Influence Functional and Cumulant Expansion
The non-Markovian behavior of open quantum systems interacting with a reservoir can often be described in terms of a time-local master equation involving a time-dependent generator which is not in Lindblad form. A systematic perturbation expansion of the generator is obtained either by means of van Kampen’s method of ordered cumulants or else by use of the Feynman — Vernon influence functional technique. Both expansions are demonstrated to yield equivalent expressions for the generator in all orders of the system-reservoir coupling. Explicit formulae are derived for the second- and the fourth-order generator in terms of the influence functional.
KeywordsOpen quantum system Non-Markovian quantum processes Influence functional Time-convolutionless projection operator technique Cumulant expansion Stochastic wavefunction method
Unable to display preview. Download preview PDF.