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Title: Mappings of open quantum systems onto chain representations and Markovian embeddings

Abstract

We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding so-called “sequence of secondary measures problem” and give them a physical interpretation.

Authors:
 [1];  [2];  [3]; ; ;  [4]
  1. QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom)
  2. (Germany)
  3. Lycée Polyvalent Rouvière, Rue Sainte Claire Deville. BP 1205, 83070 Toulon (France)
  4. Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm (Germany)
Publication Date:
OSTI Identifier:
22251164
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; INTERACTIONS; ITERATIVE METHODS; MAPPING; MARKOV PROCESS; POLYNOMIALS; SPECTRAL DENSITY

Citation Formats

Woods, M. P., E-mail: mischa.woods05@imperial.ac.uk, Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm, Groux, R., Chin, A. W., Huelga, S. F., and Plenio, M. B. Mappings of open quantum systems onto chain representations and Markovian embeddings. United States: N. p., 2014. Web. doi:10.1063/1.4866769.
Woods, M. P., E-mail: mischa.woods05@imperial.ac.uk, Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm, Groux, R., Chin, A. W., Huelga, S. F., & Plenio, M. B. Mappings of open quantum systems onto chain representations and Markovian embeddings. United States. doi:10.1063/1.4866769.
Woods, M. P., E-mail: mischa.woods05@imperial.ac.uk, Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm, Groux, R., Chin, A. W., Huelga, S. F., and Plenio, M. B. Sat . "Mappings of open quantum systems onto chain representations and Markovian embeddings". United States. doi:10.1063/1.4866769.
@article{osti_22251164,
title = {Mappings of open quantum systems onto chain representations and Markovian embeddings},
author = {Woods, M. P., E-mail: mischa.woods05@imperial.ac.uk and Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm and Groux, R. and Chin, A. W. and Huelga, S. F. and Plenio, M. B.},
abstractNote = {We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding so-called “sequence of secondary measures problem” and give them a physical interpretation.},
doi = {10.1063/1.4866769},
journal = {Journal of Mathematical Physics},
number = 3,
volume = 55,
place = {United States},
year = {Sat Mar 15 00:00:00 EDT 2014},
month = {Sat Mar 15 00:00:00 EDT 2014}
}
  • We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding so-called “sequence of secondary measures problem” and give them a physical interpretation.
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