dorsal/arxiv
View SchemaLiouville invariance in quantum and classical mechanics
| Authors | Alec Maassen van den Brink, A. M. Zagoskin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112080 |
| URL | https://arxiv.org/abs/quant-ph/0112080 |
| Journal | Quantum Information Processing_1_, 55 (2002) |
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.
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"abstract": "The density-matrix and Heisenberg formulations of quantum mechanics\nfollow--for unitary evolution--directy from the Schr\"odinger equation.\nNevertheless, the symmetries of the corresponding evolution operator, the\nLiouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This\nis due to L only involving eigenenergy_differences_, which can be degenerate\neven if the energies themselves are not. Remarkably, this possibility has\nrarely been mentioned in the literature, and never pursued more generally. We\nconsider an example involving mesoscopic Josephson devices, but the analysis\nonly assumes familiarity with basic quantum mechanics. Subsequently, such\n_L-symmetries_ are shown to occur more widely, in particular also in classical\nmechanics. The symmetry\u0027s relevance to dissipative systems and\nquantum-information processing is briefly discussed.",
"arxiv_id": "quant-ph/0112080",
"authors": [
"Alec Maassen van den Brink",
"A. M. Zagoskin"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"nlin.SI"
],
"journal_ref": "Quantum Information Processing_1_, 55 (2002)",
"title": "Liouville invariance in quantum and classical mechanics",
"url": "https://arxiv.org/abs/quant-ph/0112080"
},
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