Trace formulas for stochastic evolution operators: Weak noise perturbation theory

Details Trace formulas for stochastic evolution operators: Weak noise perturbation theory Trace formulas for stochastic evolution operators: Weak noise perturbation theory

1998-07-25

arxiv.org/abs/chao-dyn/9807034v1

J. Stat. Phys. 93, 981 (1998).

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 2 graphs and 15 Feynman diagrams imported into the text

Scientific paper

10.1023/B:JOSS.0000033173.38345.

Periodic orbit theory is an effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field theoretic formalism, and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-leading hbar corrections to the Gutzwiller trace formula, with long time averages calculated from periodic orbits of the deterministic system. The perturbative corrections are computed analytically and tested numerically on a simple 1-dimensional system.

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