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arXiv:0902.2294 · Open Systems & Information Dynamics

On the Structure of Generators for Non-Markovian Master Equations

Andrzej Kossakowski, Rolando Rebolledo

Published Aug 13, 2009• 38 citations
arXivHTMLPDF

Abstract

Complete characterization of complete positivity preserving non-Markovian master equations is presented.
DOI
10.1142/s1230161209000190

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Convolutionless and convolution master equations are the two mostly used physical descriptions of open quantum systems dynamics. We subject these equations to time deformations: local dilations and contractions of time scale. We prove that the convolutionless equation remains legitimate under any time deformation (results in a completely positive dynamical map) if and only if the original dynamics is completely positive divisible. Similarly, for a specific class of convolution master equations we show that uniform time dilations preserve positivity of the deformed map if the original map is positive divisible. These results allow witnessing different types of non-Markovian behavior: the absence of complete positivity for a deformed convolutionless master equation clearly indicates that the original dynamics is at least weakly non-Markovian; the absence of positivity for a class of time-dilated convolution master equations is a witness of essentially non-Markovian original dynamics.