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Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

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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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00102965
Contributor : Thierry Dauxois Connect in order to contact the contributor
Submitted on : Tuesday, October 3, 2006 - 9:12:49 AM
Last modification on : Tuesday, January 5, 2021 - 10:54:03 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 5:22:27 PM

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Sébastien Paulin, Angel Alastuey, Thierry Dauxois. Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation. Journal of Statistical Physics, Springer Verlag, 2007, 128 (6), pp.1391-1414. ⟨10.1007/s10955-007-9346-5⟩. ⟨ensl-00102965⟩

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