Citation

G. Palla et al., Noise corrections to stochastic trace formulas, FOUND PHYS, 31(4), 2001, pp. 641-657

Citations number

14

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Physics

Journal title

FOUNDATIONS OF PHYSICS

ISSN journal

0015-9018
â†’ ACNP

Volume

31

Issue

4

Year of publication

2001

Pages

641 - 657

Database

ISI

SICI code

0015-9018(200104)31:4<641:NCTSTF>2.0.ZU;2-B

Abstract

We review studies of an evolution operator L for a discrete Langevin equati
on with a strongly hyperbolic classical dynamics and a Gaussian noise. The
leading eigenvalue of L yields a physically measurable property of the dyna
mical system, the escape rate from the repeller. The spectrum of the evolut
ion operator L in the weak noise limit can be computed in several ways. A m
ethod using a local matrix representation of the operator allows to push th
e corrections to the escape rate zip to order eight in the noise expansion
parameter. These corrections then appear to form a divergent series. Actual
ly, via a cumulant expansion, they relate to analogous divergent series for
other quantities, the traces of the evolution operators L-n. Using an inte
gral representation of the evolution operator L, ive then investigate the h
igh order corrections to the latter traces. Their asymptotic behavior is fo
und to be controlled by sub-dominant saddle points previously neglected in
the perturbative expansion, and to be ultimately described by a kind of tra
ce formula.