dorsal/arxiv
View SchemaGeneralized Moyal structures in phase space, kinetic equations and their classical limit: II. Applications to harmonic oscillator models
| Authors | C. Tzanakis, A. P. Grecos, P. Hatjimanolaki |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9605016 |
| URL | https://arxiv.org/abs/quant-ph/9605016 |
Abstract
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium chain of other oscillators having nearest-neighbour interactions. The kinetic equation is derived without using the so called rotating-wave approximation. Then it is shown that the classical limit of the corresponding phase-space equation is independent of the ordering of operators corresponding to the inverse of the generalized Wigner transformation, provided the latter is involutive. Moreover, this limit equation, which conserves the probabilistic nature of the distribution function and obeys an H-theorem, coincides with the kinetic equation for the corresponding classical system, which is derived independently and is distinct from that usually obtained in the litterature and not sharing the above properties. Finally the same formalism is applied to more general model equations used in quantum optics and it is shown that the above results remain unaltered.
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"date_created": "2026-03-02T18:02:38.210000Z",
"date_modified": "2026-03-02T18:02:38.210000Z",
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"abstract": "The formalism of generalized Wigner transformations developped in a previous\npaper, is applied to kinetic equations of the Lindblad type for quantum\nharmonic oscillator models. It is first applied to an oscillator coupled to an\nequilibrium chain of other oscillators having nearest-neighbour interactions.\nThe kinetic equation is derived without using the so called rotating-wave\napproximation. Then it is shown that the classical limit of the corresponding\nphase-space equation is independent of the ordering of operators corresponding\nto the inverse of the generalized Wigner transformation, provided the latter is\ninvolutive. Moreover, this limit equation, which conserves the probabilistic\nnature of the distribution function and obeys an H-theorem, coincides with the\nkinetic equation for the corresponding classical system, which is derived\nindependently and is distinct from that usually obtained in the litterature and\nnot sharing the above properties. Finally the same formalism is applied to more\ngeneral model equations used in quantum optics and it is shown that the above\nresults remain unaltered.",
"arxiv_id": "quant-ph/9605016",
"authors": [
"C. Tzanakis",
"A. P. Grecos",
"P. Hatjimanolaki"
],
"categories": [
"quant-ph"
],
"title": "Generalized Moyal structures in phase space, kinetic equations and their classical limit: II. Applications to harmonic oscillator models",
"url": "https://arxiv.org/abs/quant-ph/9605016"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b5c73d9f-3378-4fff-8405-277dc0a86f6f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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