Noise corrections to stochastic trace formulas

Details Noise corrections to stochastic trace formulas Noise corrections to stochastic trace formulas

2001-01-25

arxiv.org/abs/nlin/0101045v3

Foundations of Physics, Vol. 31, No. 4 641-657 (2001)

Nonlinear Sciences

Chaotic Dynamics

21 pages, 4 figures,corrected typos

Scientific paper

We review studies of an evolution operator L for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of L yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator L in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators L^n. Using an integral representation of the evolution operator L, we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula.

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