Mappings of open quantum systems onto chain representations and Markovian embeddings

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4866769· OSTI ID:22250932

Groux, R. ^[1]; Chin, A. W.; Huelga, S. F.; Plenio, M. B. ^[2]

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1. Lycée Polyvalent Rouvière, Rue Sainte Claire Deville. BP 1205, 83070 Toulon (France)
2. Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm (Germany)

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.

• OSTI ID: 22250932
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
INTERACTIONS
ITERATIVE METHODS
MAPPING
MARKOV PROCESS
POLYNOMIALS
SPECTRAL DENSITY