dorsal/arxiv
View SchemaThe 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators
| Authors | Kirill N. Alekseev, Jan Perina |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9812019 |
| URL | https://arxiv.org/abs/quant-ph/9812019 |
| DOI | 10.1238/Physica.Regular.061a00007 |
| Journal | Physica Scripta 61(1) (2000) 7-16 |
Abstract
We develop a method for the determination of thecdynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the quantum-classical correspondence. Using this method, we find analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.
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"abstract": "We develop a method for the determination of thecdynamics of dissipative\nquantum systems in the limit of large number of quanta N, based on the\n1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the\nquantum-classical correspondence. Using this method, we find analytically the\ndynamics of nonclassical states generation in the higher-order anharmonic\ndissipative oscillators for an arbitrary temperature of a reservoir. We show\nthat the quantum correction to the classical motion increases with time\nquadratically up to some maximal value, which is dependent on the degree of\nnonlinearity and a damping constant, and then it decreases. Similarities and\ndifferences with the corresponding behavior of the quantum corrections to the\nclassical motion in the Hamiltonian chaotic systems are discussed. We also\ncompare our results obtained for some limiting cases with the results obtained\nby using other semiclassical tools and discuss the conditions for validity of\nour approach.",
"arxiv_id": "quant-ph/9812019",
"authors": [
"Kirill N. Alekseev",
"Jan Perina"
],
"categories": [
"quant-ph",
"chao-dyn",
"nlin.CD",
"physics.optics"
],
"doi": "10.1238/Physica.Regular.061a00007",
"journal_ref": "Physica Scripta 61(1) (2000) 7-16",
"title": "The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators",
"url": "https://arxiv.org/abs/quant-ph/9812019"
},
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