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Journal of Statistical Physics

, Volume 131, Issue 1, pp 51–78 | Cite as

Operator Correlations and Quantum Regression Theorem in Non-Markovian Lindblad Rate Equations

  • Adrián A. Budini
Article

Abstract

Non-Markovian Lindblad rate equations arise from alternative microscopic interactions such as quantum systems coupled to composite reservoirs, where extra degrees of freedom mediate the interaction between the system and a Markovian reservoir, as well as from systems coupled to complex structured reservoirs whose action can be well approximated by a direct sum of Markovian sub-reservoirs (Budini in Phys. Rev. A 74:053815 [2006]). The purpose of this paper is two fold. First, for both kinds of interactions we find general expressions for the system operator correlations written in terms of the Lindblad rate propagator. Secondly, we find the conditions under which a quantum regression hypothesis is valid. We show that a non-Markovian quantum regression theorem can only be granted in a stationary regime, being a necessary condition the fulfillment of a detailed balance condition. This result is independent of the underlying microscopic interaction, providing a criterion for the validity of the regression hypothesis in non-Markovian Lindblad-like master equations. As an example, we study the correlations of a two-level system coupled to different kind of reservoirs.

Keywords

Non-Markovian open quantum system dynamics Quantum regression theorem 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Consejo Nacional de Investigaciones Científicas y TécnicasCentro Atómico BarilocheBarilocheArgentina

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