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Title: Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field

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.

Authors:
 [1];  [2];  [3]; ;  [1];  [2];  [4]
  1. 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)
  2. (Germany)
  3. (Romania), E-mail: eliadestefanescu@yahoo.fr
  4. (Romania)
Publication Date:
OSTI Identifier:
21163690
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 323; Journal Issue: 5; Other Information: DOI: 10.1016/j.aop.2008.01.009; PII: S0003-4916(08)00011-0; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION SPECTRA; APPROXIMATIONS; BLOCH EQUATIONS; BOSONS; ELECTROMAGNETIC FIELDS; ENERGY-LEVEL TRANSITIONS; FERMIONS; MARKOV PROCESS; MATHEMATICAL EVOLUTION; QUANTUM DOTS; SELF-CONSISTENT FIELD

Citation Formats

Stefanescu, Eliade, Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Scheid, Werner, Sandulescu, Aurel, Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen, and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest. Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field. United States: N. p., 2008. Web. doi:10.1016/j.aop.2008.01.009.
Stefanescu, Eliade, Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Scheid, Werner, Sandulescu, Aurel, Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen, & Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest. Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field. United States. doi:10.1016/j.aop.2008.01.009.
Stefanescu, Eliade, Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Scheid, Werner, Sandulescu, Aurel, Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen, and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest. Thu . "Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field". United States. doi:10.1016/j.aop.2008.01.009.
@article{osti_21163690,
title = {Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field},
author = {Stefanescu, Eliade and Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest and Scheid, Werner and Sandulescu, Aurel and Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest},
abstractNote = {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.},
doi = {10.1016/j.aop.2008.01.009},
journal = {Annals of Physics (New York)},
number = 5,
volume = 323,
place = {United States},
year = {Thu May 15 00:00:00 EDT 2008},
month = {Thu May 15 00:00:00 EDT 2008}
}
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