Mappings of open quantum systems onto chain representations and Markovian embeddings

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 unde...

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Bibliographic Details
Published in:Journal of mathematical physics 2014-03, Vol.55 (3), p.1
Main Authors: Woods, M. P., Groux, R., Chin, A. W., Huelga, S. F., Plenio, M. B.
Format: Article
Language:English
Subjects:
Asymptotic methods
ASYMPTOTIC SOLUTIONS
Chains
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Density
Embedded systems
INTERACTIONS
ITERATIVE METHODS
MAPPING
Markov chains
MARKOV PROCESS
Oscillators
Physics
POLYNOMIALS
SPECTRAL DENSITY
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4866769