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Zbl 1152.82322
Stefanescu, Eliade; Scheid, Werner; Sandulescu, Aurel
Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field. (English)
[J] Ann. Phys. 323, No. 5, 1168-1190 (2008). ISSN 0003-4916

Summary: For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad's form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.

MSC 2000:: *82C31 Stochastic methods in time-dependent statistical mechanics
81S25 Quantum stochastic calculus

Keywords: master equation; non-Markovian; Maxwell-Bloch equations; absorption spectrum

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Zentralblatt MATH Berlin [Germany]