Two examples of Quantum Dynamical Semigroups

Małgorzata Bodzioch; Joachim Domsta

doi:10.1142/s1230161211000091

Two examples of Quantum Dynamical Semigroups

Abstract

The Hamiltonians of the considered bi-partite systems are of the form $$ H_{S,R} = H_S /times 1_R + Q_{S} /times M_R + 1_S /times H_R $$ Subindex $S$ corresponds to the observed system and $R$ to the reservoir (the enviroment of $S$). Two classes of systems are distinguished: the discrete-continuous (D-C) and the continuous-continuous (C-C) models. In both cases resevoir operators $M_R$ and $H_R$ are of continuous spectrum type. In D-C models the operators $H_S$ and $Q_S$ possess discrete spectra. In C-C models, the operators $H_S$ and $Q_S$ are of continuous spectrum type. In each case of our examples the semigroup property for the reduced dynamics of system $S$ is obtained under particular circumstances, depending on the diagonal of the density matrix of the reference state for $R$. In D-C models, due to discrete spectrum of $Q_S$, the semigroup property of the reduced dynamics of the reservoir $R$ is shown to be impossible, unless the coupling to $S$ is trivial.

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: OPEN SYSTEMS & INFORMATION DYNAMICS no. 18, pages 143 - 155,
ISSN: 1230-1612
Language:: English
Publication year:: 2011
Bibliographic description:: Bodzioch M., Domsta J.: Two examples of Quantum Dynamical Semigroups// OPEN SYSTEMS & INFORMATION DYNAMICS. -Vol. 18, nr. Iss. 2 (2011), s.143-155
DOI:: Digital Object Identifier (open in new tab) 10.1142/s1230161211000091
Verified by:: Gdańsk University of Technology