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Download fileLiouville invariance in quantum and classical mechanics
journal contribution
posted on 2015-12-17, 11:28 authored by Alec Maassen van den Brink, Alexandre ZagoskinAlexandre ZagoskinThe 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.
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School
- Science
Department
- Physics
Published in
Quantum Information Processing_1_, 55 (2002)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.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2002Notes
The final publication is available at Springer via http://dx.doi.org/10.1023/A:1019657303471 .ISSN
1570-0755eISSN
1573-1332Publisher version
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- en