Liouville invariance in quantum and classical mechanics
journal contributionposted on 2015-12-17, 11:28 authored 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.
Published inQuantum Information Processing_1_, 55 (2002)
CitationMAASSEN 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.
- AM (Accepted Manuscript)
Publisher statementThis 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/
NotesThe final publication is available at Springer via http://dx.doi.org/10.1023/A:1019657303471 .