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Title: Liouville invariance in quantum and classical mechanics
Authors: Maassen van den Brink, Alec
Zagoskin, Alexandre M.
Keywords: Symmetry
Superoperators
Phase-space flow
Issue Date: 2002
Publisher: © Springer
Citation: MAASSEN VAN DEN BRINK, A. and ZAGOSKIN, A.M., 2002. Liouville invariance in quantum and classical mechanics. Quantum Information Processing, 1(1-2), pp 55-72.
Abstract: The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This is due to L only involving eigenenergy_differences_, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has rarely been mentioned in the literature, and never pursued more generally. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such _L-symmetries_ are shown to occur more widely, in particular also in classical mechanics. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed.
Description: The final publication is available at Springer via http://dx.doi.org/10.1023/A:1019657303471 .
Version: Accepted for publication
DOI: 10.1023/A:1019657303471
URI: https://dspace.lboro.ac.uk/2134/19899
Publisher Link: http://dx.doi.org/10.1023/A:1019657303471
ISSN: 1570-0755
Appears in Collections:Published Articles (Physics)

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