NonMarkovian 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 nonMarkovian master equation in the secondorder approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the wellknown 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 nonMarkovian terms proceeding from the fluctuations of the selfconsistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the selfconsistent field of the environment, and the influence of the timeevolution 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 nonMarkovian MaxwellBloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of twolevel quantum dots.
 Authors:
 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)
 (Germany)
 (Romania), Email: eliadestefanescu@yahoo.fr
 (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: S00034916(08)000110; 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; ENERGYLEVEL TRANSITIONS; FERMIONS; MARKOV PROCESS; MATHEMATICAL EVOLUTION; QUANTUM DOTS; SELFCONSISTENT FIELD
Citation Formats
Stefanescu, Eliade, Institut fuer Theoretische Physik der JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Scheid, Werner, Sandulescu, Aurel, Institut fuer Theoretische Physik der JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen, and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest. NonMarkovian 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 JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Scheid, Werner, Sandulescu, Aurel, Institut fuer Theoretische Physik der JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen, & Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest. NonMarkovian 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 JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Scheid, Werner, Sandulescu, Aurel, Institut fuer Theoretische Physik der JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen, and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest. Thu .
"NonMarkovian 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 = {NonMarkovian master equation for a system of Fermions interacting with an electromagnetic field},
author = {Stefanescu, Eliade and Institut fuer Theoretische Physik der JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 Giessen and Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest and Scheid, Werner and Sandulescu, Aurel and Institut fuer Theoretische Physik der JustusLiebigUniversitaet, HeinrichBuffRing 16, D35392 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 nonMarkovian master equation in the secondorder approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the wellknown 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 nonMarkovian terms proceeding from the fluctuations of the selfconsistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the selfconsistent field of the environment, and the influence of the timeevolution 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 nonMarkovian MaxwellBloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of twolevel 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}
}

We consider the exact reduced dynamics of a twolevel system coupled to a bosonic reservoir, further obtaining the exact timeconvolutionless and NakajimaZwanzig nonMarkovian equations of motion. The system considered includes the damped and undamped JaynesCummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and the timeconvolutionless generator as well as the NakajimaZwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact timeconvolutionless master equation is multiplied by a different timedependent function. Similarly, in the NakajimaZwanzigmore »

Nonequilibrium effects upon the nonMarkovian CaldeiraLeggett quantum master equation
Highlights: > Classical Brownian motion described by a nonMarkovian FokkerPlanck equation. > Quantization process. > Quantum Brownian motion described by a nonMarkovian CaldeiraLeggett equation. > A nonequilibrium quantum thermal force is predicted.  Abstract: We obtain a nonMarkovian quantum master equation directly from the quantization of a nonMarkovian FokkerPlanck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a nonthermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a nonMarkovian CaldeiraLeggett master equation on the basis of which we work out the conceptmore » 
Generalized Master Equation with NonMarkovian Multichromophoric Förster Resonance Energy Transfer for Modular Exciton Densities
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GMEMED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a nonMarkovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GMEMED for four sites of the FennaMatthewsOlson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately describedmore » 
Densitymatrix operatorial solution of the nonMarkovian master equation for quantum Brownian motion
An original method to exactly solve the nonMarkovian master equation describing the interaction of a single harmonic oscillator with a quantum environment in the weakcoupling limit is reported. By using a superoperatorial approach, we succeed in deriving the operatorial solution for the density matrix of the system. Our method is independent of the physical properties of the environment. We show the usefulness of our solution deriving explicit expressions for the dissipative time evolution of some observables of physical interest for the system, such as, for example, its mean energy. 
NonMarkovian dissipative dynamics of two coupled qubits in independent reservoirs: Comparison between exact solutions and masterequation approaches
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The oneexcitation dynamics is derived and compared with that based on the resolution of appropriate nonMarkovian master equations. The NakajimaZwanzig and the timeconvolutionless projection operator techniques are exploited to provide a description of the nonMarkovian features of the dynamics of the twoqubit system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.