Time-local master equations: influence functional and cumulant expansion
Abstract
The non-Markovian behaviour 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-reservor coupling. Explicit formulae are derived for the second and the fourth order generator in terms of the influence functional.
Cite
@article{arxiv.quant-ph/0209153,
title = {Time-local master equations: influence functional and cumulant expansion},
author = {Heinz-Peter Breuer and Andrea Ma and Francesco Petruccione},
journal= {arXiv preprint arXiv:quant-ph/0209153},
year = {2007}
}
Comments
10 pages, to be published in Quantum Computing and Quantum Bits in Mesoscopic Systems (Kluwer Academic Plenum Publishers, december 2002)