dorsal/arxiv
View SchemaAnalysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation
| Authors | Sébastien Paulin, Angel Alastuey, Thierry Dauxois |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610016 |
| URL | https://arxiv.org/abs/quant-ph/0610016 |
| DOI | 10.1007/s10955-007-9346-5 |
| Journal | Journal of Statistical Physics 128, 1391-1414 (2007) |
Abstract
We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail.
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"abstract": "We study the low temperature behaviour of path integrals for a simple\none-dimensional model. Starting from the Feynman-Kac formula, we derive a new\nfunctional representation of the density matrix at finite temperature, in terms\nof the occupation times of Brownian motions constrained to stay within boxes\nwith finite sizes. From that representation, we infer a kind of ergodic\napproximation, which only involves double ordinary integrals. As shown by its\napplications to different confining potentials, the ergodic approximation turns\nout to be quite efficient, especially in the low-temperature regime where other\nusual approximations fail.",
"arxiv_id": "quant-ph/0610016",
"authors": [
"S\u00e9bastien Paulin",
"Angel Alastuey",
"Thierry Dauxois"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1007/s10955-007-9346-5",
"journal_ref": "Journal of Statistical Physics 128, 1391-1414 (2007)",
"title": "Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation",
"url": "https://arxiv.org/abs/quant-ph/0610016"
},
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