dorsal/arxiv
View SchemaSemiclassical Series at Finite Temperature
| Authors | C. A. A. de Carvalho, R. M. Cavalcanti, E. S. Fraga, S. E. Joras |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810045 |
| URL | https://arxiv.org/abs/quant-ph/9810045 |
| DOI | 10.1006/aphy.1998.5900 |
| Journal | Annals Phys. 273 (1999) 146-170 |
Abstract
We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral representation of the partition function, and we present a systematic procedure to generate the terms of the series using the minima of the Euclidean action as the only input. For the particular case of a quartic anharmonic oscillator, we compute the first two terms of the series, and investigate their high and low temperature limits. We also exhibit the nonperturbative character of the terms, as each corresponds to sums over infinite subsets of perturbative graphs. We illustrate the power of such resummations by extracting from the first term an accurate nonperturbative estimate of the ground-state energy of the system and a curve for the specific heat. We conclude by pointing out possible extensions of our results which include field theories with spherically symmetric classical solutions.
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"abstract": "We derive the semiclassical series for the partition function of a\none-dimensional quantum-mechanical system consisting of a particle in a\nsingle-well potential. We do this by applying the method of steepest descent to\nthe path-integral representation of the partition function, and we present a\nsystematic procedure to generate the terms of the series using the minima of\nthe Euclidean action as the only input. For the particular case of a quartic\nanharmonic oscillator, we compute the first two terms of the series, and\ninvestigate their high and low temperature limits. We also exhibit the\nnonperturbative character of the terms, as each corresponds to sums over\ninfinite subsets of perturbative graphs. We illustrate the power of such\nresummations by extracting from the first term an accurate nonperturbative\nestimate of the ground-state energy of the system and a curve for the specific\nheat. We conclude by pointing out possible extensions of our results which\ninclude field theories with spherically symmetric classical solutions.",
"arxiv_id": "quant-ph/9810045",
"authors": [
"C. A. A. de Carvalho",
"R. M. Cavalcanti",
"E. S. Fraga",
"S. E. Joras"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th"
],
"doi": "10.1006/aphy.1998.5900",
"journal_ref": "Annals Phys. 273 (1999) 146-170",
"title": "Semiclassical Series at Finite Temperature",
"url": "https://arxiv.org/abs/quant-ph/9810045"
},
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