Analysis of Path Integrals at Low Temperature: Box Formula,Occupation Time and Ergodic Approximation |
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Authors: | Sébastien Paulin Angel Alastuey Thierry Dauxois |
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Institution: | (1) Laboratoire de Physique, CNRS, ENS Lyon, 46 allée d’Italie, 69364 Lyon, cédex 07, France |
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Abstract: | We study the low temperature behavior 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 for 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 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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Keywords: | |
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