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Liouville invariance in quantum and classical mechanics

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journal contribution
posted on 17.12.2015, 11:28 by Alec Maassen van den Brink, Alexandre ZagoskinAlexandre Zagoskin
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.

History

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

© Springer

Version

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

2002

Notes

The final publication is available at Springer via http://dx.doi.org/10.1023/A:1019657303471 .

ISSN

1570-0755

eISSN

1573-1332

Language

en