Trace formulas for stochastic evolution operators: Smooth conjugation method

Details Trace formulas for stochastic evolution operators: Smooth conjugation method Trace formulas for stochastic evolution operators: Smooth conjugation method

1998-10-30

arxiv.org/abs/chao-dyn/9811003v1

Nonlinearity 12, 939 (1999)

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 1 figure, New techniques and results for a problem we considered in chao-dyn/9807034

Scientific paper

10.1088/0951-7715/12/4/312

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 neighborhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transfered 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 analog of the Gutzwiller trace formula with the ``hbar'' corrections computed an order higher than what has so far been attainable in stochastic and quantum-mechanical applications.

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