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.
CITATION STYLE
Breuer, H.-P., Ma, A., & Petruccione, F. (2004). Time-Local Master Equations: Influence Functional and Cumulant Expansion. In Quantum Computing and Quantum Bits in Mesoscopic Systems (pp. 263–271). Springer US. https://doi.org/10.1007/978-1-4419-9092-1_29
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