dorsal/arxiv
View SchemaTunneling catastrophes of the partition function
| Authors | C. A. A. de Carvalho, R. M. Cavalcanti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9803049 |
| URL | https://arxiv.org/abs/quant-ph/9803049 |
| Journal | Braz.J.Phys. 27 (1997) 373-378 |
Abstract
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths may appear, including tunneling paths. The transition from single to multiple-path regime corresponds to well-defined catastrophes. Tunneling sets in whenever they occur. Our formula fully accounts for this feature.
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"abstract": "We use path-integrals to derive a general expression for the semiclassical\napproximation to the partition function of a one-dimensional quantum-mechanical\nsystem. Our expression depends solely on ordinary integrals which involve the\npotential. For high temperatures, the semiclassical expression is dominated by\nsingle closed paths. As we lower the temperature, new closed paths may appear,\nincluding tunneling paths. The transition from single to multiple-path regime\ncorresponds to well-defined catastrophes. Tunneling sets in whenever they\noccur. Our formula fully accounts for this feature.",
"arxiv_id": "quant-ph/9803049",
"authors": [
"C. A. A. de Carvalho",
"R. M. Cavalcanti"
],
"categories": [
"quant-ph"
],
"journal_ref": "Braz.J.Phys. 27 (1997) 373-378",
"title": "Tunneling catastrophes of the partition function",
"url": "https://arxiv.org/abs/quant-ph/9803049"
},
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