Spectrum of stochastic evolution operators: Local matrix representation approach

Predrag Cvitanović, Niels Søndergaard, Gergely Palla, G. Vattay, C. P. Dettmann

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

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 results 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.

Original languageEnglish
Pages (from-to)3936-3941
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume60
Issue number4
DOIs
Publication statusPublished - Jan 1 1999

Fingerprint

Evolution Operator
Matrix Representation
Feynman Diagrams
operators
Stochastic Flow
Feynman diagrams
Additive Noise
matrices
determinants
Periodic Orbits
Perturbation Theory
Determinant
perturbation theory
analogs
Analogue
orbits
expansion
evaluation
Evaluation
Standards

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Spectrum of stochastic evolution operators : Local matrix representation approach. / Cvitanović, Predrag; Søndergaard, Niels; Palla, Gergely; Vattay, G.; Dettmann, C. P.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 60, No. 4, 01.01.1999, p. 3936-3941.

Research output: Contribution to journalArticle

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