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Title: Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system

Abstract

We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes-Cummings 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 time-convolutionless generator as well as the Nakajima-Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important differences.

Authors:
;  [1]
  1. Dipartimento di Fisica, Universita degli Studi di Milano, Via Celoria 16, I-20133 Milano (Italy)
Publication Date:
OSTI Identifier:
21448437
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.82.022110; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; BOSONS; ENERGY LEVELS; EQUATIONS OF MOTION; KERNELS; MARKOV PROCESS; MATRICES; QUANTUM MECHANICS; QUANTUM OPERATORS; QUANTUM STATES; TIME DEPENDENCE; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL OPERATORS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC PROCESSES

Citation Formats

Smirne, Andrea, Vacchini, Bassano, and Sezione di Milano, INFN, Via Celoria 16, I-20133 Milano. Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.82.022110.
Smirne, Andrea, Vacchini, Bassano, & Sezione di Milano, INFN, Via Celoria 16, I-20133 Milano. Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system. United States. https://doi.org/10.1103/PHYSREVA.82.022110
Smirne, Andrea, Vacchini, Bassano, and Sezione di Milano, INFN, Via Celoria 16, I-20133 Milano. Sun . "Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system". United States. https://doi.org/10.1103/PHYSREVA.82.022110.
@article{osti_21448437,
title = {Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system},
author = {Smirne, Andrea and Vacchini, Bassano and Sezione di Milano, INFN, Via Celoria 16, I-20133 Milano},
abstractNote = {We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes-Cummings 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 time-convolutionless generator as well as the Nakajima-Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important differences.},
doi = {10.1103/PHYSREVA.82.022110},
url = {https://www.osti.gov/biblio/21448437}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 82,
place = {United States},
year = {2010},
month = {8}
}