Abstract
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.
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Breuer, HP., Ma, A., Petruccione, F. (2004). Time-Local Master Equations: Influence Functional and Cumulant Expansion. In: Leggett, A.J., Ruggiero, B., Silvestrini, P. (eds) Quantum Computing and Quantum Bits in Mesoscopic Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9092-1_29
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DOI: https://doi.org/10.1007/978-1-4419-9092-1_29
Publisher Name: Springer, Boston, MA
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