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The dynamics of open quantum systems: accessibility results
Author(s) -
Kurniawan I.,
Dirr G.,
Helmke U.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701089
Subject(s) - master equation , lie algebra , quantum , transitive relation , unital , simple (philosophy) , pure mathematics , mathematics , relaxation (psychology) , focus (optics) , mathematical physics , physics , algebra over a field , quantum mechanics , combinatorics , psychology , social psychology , philosophy , epistemology , optics
In this paper we study the accessibility properties of finite dimensional (N‐level) open quantum systems in the presence of dissipation and relaxation described by the Lindblad master equation. We specifically focus on the unital Lindbladian case where general results can be obtained. The theory of transitive Lie‐group actions is used to classify the system Lie‐algebras of the Lindblad equation for which the reachable sets have nonempty interior. For the special case of n ‐coupled spin‐1/2 systems, we obtain a particularly simple characterization. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)