IJPAM: Volume 102, No. 3 (2015)

ON A QUANTUM SYSTEM EXPOSED TO A HEAT BATH

Eugen Grycko$^1$, Werner Kirsch$^2$, Tobias Mühlenbruch$^3$
$^{1,2,3}$Department of Mathematics and Computer Science
University of Hagen
Universitätsstrasse 1
D-58084 Hagen, GERMANY


Abstract. An appropriate generator matrix induces in a natural way a Markov semigroup which can be applied to the construction of a continuous time Markov process whose asymptotic distribution is independent of the initial state. We propose a generator associated with a prescribed (arbitrary) distribution which turns out to be reversible for the corresponding Markov process. As an application, we show that the Markov process offers a physically plausible description of a quantum system exposed to a heat bath. The system approaches its Gibbs state corresponding to the temperature of the heat bath if its initial state commutes with the Hamiltonian.

Received: May 8, 2015

AMS Subject Classification: 82C10, 60J27

Key Words and Phrases: fixed point theorem, Doob's theorem, homogeneous Markov process

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DOI: 10.12732/ijpam.v102i3.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 3
Pages: 533 - 545


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