Spectrum of stochastic evolution operators: Local matrix representation approach

Details Spectrum of stochastic evolution operators: Local matrix representation approach Spectrum of stochastic evolution operators: Local matrix representation approach

1999-04-14

arxiv.org/abs/chao-dyn/9904027v1

Phys. Rev. E 60, 3936 (1999).

Nonlinear Sciences

Chaotic Dynamics

7 pages, 2 figures, Third approach to a problem we considered in chao-dyn/9807034 and chao-dyn/9811003

Scientific paper

10.1103/PhysRevE.60.3936

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The result are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.

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