Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation - ENS de Lyon - École normale supérieure de Lyon Access content directly
Journal Articles Journal of Statistical Physics Year : 2007

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.
Fichier principal
Vignette du fichier
article1.pdf (476.75 Ko) Télécharger le fichier

Dates and versions

ensl-00102965 , version 1 (03-10-2006)

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook Twitter LinkedIn More