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Completely positive maps with memory

Sonja Daffer·Krzysztof Wodkiewicz·James D. Cresser·John K. McIver
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Abstract

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. This paper examines master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel. A physical model that possesses such an exponential memory kernel is presented. This model contains a classical, fluctuating environment based on random telegraph signal stochastic variables.

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Sonja Daffer, Krzysztof Wodkiewicz, James D. Cresser, John K. McIver. 2003-09-09. Completely positive maps with memory. https://doi.org/10.1103/physreva.70.010304

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