dorsal/arxiv
View SchemaThe Quantum Canonical Ensemble
| Authors | D. C. Brody, L. P. Hughston |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9709048 |
| URL | https://arxiv.org/abs/quant-ph/9709048 |
| DOI | 10.1063/1.532661 |
| Journal | J.Math.Phys. 39 (1998) 6502-6508 |
Abstract
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as generating a Hamiltonian dynamics. Based upon the geometric structure of the quantum phase space we introduce the corresponding natural microcanonical and canonical ensembles. The resulting density matrix for the canonical ensemble differs from density matrix of the conventional approach. As an illustration, the results are applied to the case of a spin one-half particle in a heat bath with an applied magnetic field.
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"abstract": "The phase space of quantum mechanics can be viewed as the complex projective\nspace endowed with a Kaehlerian structure given by the Fubini-Study metric and\nan associated symplectic form. We can then interpret the Schrodinger equation\nas generating a Hamiltonian dynamics. Based upon the geometric structure of the\nquantum phase space we introduce the corresponding natural microcanonical and\ncanonical ensembles. The resulting density matrix for the canonical ensemble\ndiffers from density matrix of the conventional approach. As an illustration,\nthe results are applied to the case of a spin one-half particle in a heat bath\nwith an applied magnetic field.",
"arxiv_id": "quant-ph/9709048",
"authors": [
"D. C. Brody",
"L. P. Hughston"
],
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"quant-ph"
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"doi": "10.1063/1.532661",
"journal_ref": "J.Math.Phys. 39 (1998) 6502-6508",
"title": "The Quantum Canonical Ensemble",
"url": "https://arxiv.org/abs/quant-ph/9709048"
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