Trace formulae for stochastic evolution operators: Smooth conjugation method

Predrag Cvitanoví, C. P. Dettmann, Ronnie Mainieri, Gábor Vattay

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighbourhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transferred to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analogue of the Gutzwiller trace formula with the '(latin small letter h with stroke)' corrections computed an order higher than what has so far been attainable in stochastic and quantum mechanical applications.

Original languageEnglish
Pages (from-to)939-953
Number of pages15
JournalNonlinearity
Volume12
Issue number4
DOIs
Publication statusPublished - Jul 1 1999

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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