dorsal/arxiv
View SchemaPurity and decoherence in the theory of a damped harmonic oscillator
| Authors | A. Isar, A. Sandulescu, W. Scheid |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606134 |
| URL | https://arxiv.org/abs/quant-ph/0606134 |
| DOI | 10.1103/PhysRevE.60.6371 |
| Journal | Phys. Rev. E, v. 60, p. 6371 (1999) |
Abstract
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude and weak coupling cases, Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with constant in time variances. For pure states, the generalized nonlinear Schr\" odinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, the correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the considered particular models, the expressions of the rate of entropy production is written and it is shown that the states which preserve their purity in time are also the states which minimize the entropy production and, therefore, they are the most stable ones under evolution in the presence of the environment and play an important role in the description of decoherence phenomenon.
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"abstract": "For the generalized master equations derived by Karrlein and Grabert for the\nmicroscopic model of a damped harmonic oscillator, the conditions for purity of\nstates are written, in particular for different initial conditions and\ndifferent types of damping, including Ohmic, Drude and weak coupling cases,\nAgarwal and Weidlich-Haake models. It is shown that the states which remain\npure are the squeezed states with constant in time variances. For pure states,\nthe generalized nonlinear Schr\\\" odinger-type equations corresponding to these\nmaster equations are also obtained. Then the condition for purity of states of\na damped harmonic oscillator is considered in the framework of Lindblad theory\nfor open quantum systems. For a special choice of the environment coefficients,\nthe correlated coherent states with constant variances and covariance are shown\nto be the only states which remain pure all the time during the evolution of\nthe considered system. In Karrlein-Grabert and Lindblad models, as well as in\nthe considered particular models, the expressions of the rate of entropy\nproduction is written and it is shown that the states which preserve their\npurity in time are also the states which minimize the entropy production and,\ntherefore, they are the most stable ones under evolution in the presence of the\nenvironment and play an important role in the description of decoherence\nphenomenon.",
"arxiv_id": "quant-ph/0606134",
"authors": [
"A. Isar",
"A. Sandulescu",
"W. Scheid"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.60.6371",
"journal_ref": "Phys. Rev. E, v. 60, p. 6371 (1999)",
"title": "Purity and decoherence in the theory of a damped harmonic oscillator",
"url": "https://arxiv.org/abs/quant-ph/0606134"
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