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Title: Exact master equations for the non-Markovian decay of a qubit

Abstract

Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.

Authors:
 [1];  [2]
  1. Universita degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, I-20133 Milano (Italy)
  2. Physikalisches Institut, Universitaet Freiburg, Hermann-Herder Strasse 3, D-79104 Freiburg (Germany)
Publication Date:
OSTI Identifier:
21413320
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 81; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.81.042103; (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; COMPARATIVE EVALUATIONS; CONVERGENCE; DECAY; EQUATIONS; EXACT SOLUTIONS; KERNELS; MARKOV PROCESS; PERTURBATION THEORY; SIMULATION; EVALUATION; MATHEMATICAL SOLUTIONS; STOCHASTIC PROCESSES

Citation Formats

Vacchini, Bassano, Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano, and Breuer, Heinz-Peter. Exact master equations for the non-Markovian decay of a qubit. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.81.042103.
Vacchini, Bassano, Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano, & Breuer, Heinz-Peter. Exact master equations for the non-Markovian decay of a qubit. United States. https://doi.org/10.1103/PHYSREVA.81.042103
Vacchini, Bassano, Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano, and Breuer, Heinz-Peter. Thu . "Exact master equations for the non-Markovian decay of a qubit". United States. https://doi.org/10.1103/PHYSREVA.81.042103.
@article{osti_21413320,
title = {Exact master equations for the non-Markovian decay of a qubit},
author = {Vacchini, Bassano and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano and Breuer, Heinz-Peter},
abstractNote = {Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.},
doi = {10.1103/PHYSREVA.81.042103},
url = {https://www.osti.gov/biblio/21413320}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 81,
place = {United States},
year = {2010},
month = {4}
}