Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field |
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Authors: | Eliade Stefanescu Werner Scheid Aurel Sandulescu |
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Institution: | Center of Advanced Studies in Physics at the Institute of Mathematics Simion Stoilow of the Romanian Academy, 13 Calea 13 Septembrie, 050711 Bucharest S5, Romania Institut für Theoretische Physik der Justus-Liebig-Universität, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania |
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Abstract: | 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. |
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Keywords: | 03 65 Ca |
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