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Journal article
Generators of quantum Markov semigroups
Journal of mathematical physics, v 56(8), 083512
01 Aug 2015
Abstract
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works of Lindblad [Commun. Math. Phys. 48, 119-130 (1976)], Stinespring [Proc. Am. Math. Soc. 6, 211-216 (1955)], and Kraus [Ann. Phys. 64, 311-335 (1970)] imply that the generator of the semigroup has the form L(A) = Sigma V-infinity(n-1)n*AV(n) + GA + AG*, where V-n and G are elements of the underlying operator algebra. In the present paper, we investigate the form of the generators of QMSs which are not necessarily uniformly continuous and act on the bounded operators of a Hilbert space. We prove that the generators of such semigroups have forms that reflect the results of Lindblad and Stinespring. We also make some progress towards forms reflecting Kraus' result. Finally, we look at several examples to clarify our findings and verify that some of the unbounded operators we are using have dense domains. (C) 2015 AIP Publishing LLC.
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Details
- Title
- Generators of quantum Markov semigroups
- Creators
- George Androulakis - University of South CarolinaMatthew Ziemke - University of South Carolina
- Publication Details
- Journal of mathematical physics, v 56(8), 083512
- Publisher
- Amer Inst Physics
- Number of pages
- 16
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000360654800036
- Scopus ID
- 2-s2.0-84940399418
- Other Identifier
- 991021866899604721
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- Web of Science research areas
- Physics, Mathematical