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Time-local master equations: influence functional and cumulant expansion

Heinz-Peter Breuer·Andrea Ma·Francesco Petruccione
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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.

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Heinz-Peter Breuer, Andrea Ma, Francesco Petruccione. 2002-09-27. Time-local master equations: influence functional and cumulant expansion. https://arxiv.org/abs/quant-ph/0209153

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