dorsal/arxiv
View SchemaTime evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques
| Authors | J. G. Peixoto de Faria |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512060 |
| URL | https://arxiv.org/abs/quant-ph/0512060 |
| DOI | 10.1140/epjd/e2006-00278-8 |
| Journal | European Physical Journal D 42, 153-162 (2007) |
Abstract
We present the general solutions for the classical and quantum dynamics of the anharmonic oscillator coupled to a purely diffusive environment. In both cases, these solutions are obtained by the application of the Baker-Campbell-Hausdorff (BCH) formulas to expand the evolution operator in an ordered product of exponentials. Moreover, we obtain an expression for the Wigner function in the quantum version of the problem. We observe that the role played by diffusion is to reduce or to attenuate the the characteristic quantum effects yielded by the nonlinearity, as the appearance of coherent superpositions of quantum states (Schr\"{o}dinger cat states) and revivals.
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"abstract": "We present the general solutions for the classical and quantum dynamics of\nthe anharmonic oscillator coupled to a purely diffusive environment. In both\ncases, these solutions are obtained by the application of the\nBaker-Campbell-Hausdorff (BCH) formulas to expand the evolution operator in an\nordered product of exponentials. Moreover, we obtain an expression for the\nWigner function in the quantum version of the problem. We observe that the role\nplayed by diffusion is to reduce or to attenuate the the characteristic quantum\neffects yielded by the nonlinearity, as the appearance of coherent\nsuperpositions of quantum states (Schr\\\"{o}dinger cat states) and revivals.",
"arxiv_id": "quant-ph/0512060",
"authors": [
"J. G. Peixoto de Faria"
],
"categories": [
"quant-ph"
],
"doi": "10.1140/epjd/e2006-00278-8",
"journal_ref": "European Physical Journal D 42, 153-162 (2007)",
"title": "Time evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques",
"url": "https://arxiv.org/abs/quant-ph/0512060"
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