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Title: On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models

Abstract

We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima-Zwanzig's projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove's limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.

Authors:
 [1];  [2];  [3];  [4];  [5];  [5];  [5];  [6];  [4]
  1. Department of Physics, Waseda University, Tokyo 169-8555 (Japan). E-mail: kazuya.yuasa@aist.go.jp
  2. Department of Applied Physics and Advanced Institute for Complex Systems, Waseda University, Tokyo 169-8555 (Japan)
  3. Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy)
  4. (Italy)
  5. Department of Physics, Waseda University, Tokyo 169-8555 (Japan)
  6. Dipartimento di Fisica, Universita di Bari, I-70126 Bari (Italy)
Publication Date:
OSTI Identifier:
20976738
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 3; Other Information: DOI: 10.1016/j.aop.2006.06.003; PII: S0003-4916(06)00134-5; Copyright (c) 2006 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; APPROXIMATIONS; CORRELATIONS; EQUATIONS; FACTORIZATION; FORM FACTORS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; PARTICLE INTERACTIONS; QUANTUM MECHANICS

Citation Formats

Yuasa, K., Tasaki, S., Facchi, P., Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Kimura, G., Nakazato, H., Ohba, I., Pascazio, S., and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari. On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models. United States: N. p., 2007. Web. doi:10.1016/j.aop.2006.06.003.
Yuasa, K., Tasaki, S., Facchi, P., Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Kimura, G., Nakazato, H., Ohba, I., Pascazio, S., & Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari. On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models. United States. doi:10.1016/j.aop.2006.06.003.
Yuasa, K., Tasaki, S., Facchi, P., Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Kimura, G., Nakazato, H., Ohba, I., Pascazio, S., and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari. Thu . "On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models". United States. doi:10.1016/j.aop.2006.06.003.
@article{osti_20976738,
title = {On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models},
author = {Yuasa, K. and Tasaki, S. and Facchi, P. and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari and Kimura, G. and Nakazato, H. and Ohba, I. and Pascazio, S. and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari},
abstractNote = {We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima-Zwanzig's projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove's limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.},
doi = {10.1016/j.aop.2006.06.003},
journal = {Annals of Physics (New York)},
number = 3,
volume = 322,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}