Trace formula for activated escape in noisy maps

TL;DR

This paper derives a formula for calculating the noise-induced escape rate in one-dimensional noisy maps using path-integral and trace formula methods, connecting fixed points via heteroclinic orbits.

Contribution

It introduces a novel approach combining trace formulas and heteroclinic orbit analysis to compute escape rates in noisy dynamical systems.

Findings

Derived an explicit formula for escape rate in noisy maps.

Connected escape dynamics to heteroclinic orbit loops.

Provided a prefactor expression for the Arrhenius-like exponential escape rate.

Abstract

Using path-integral methods, a formula is deduced for the noise-induced escape rate from an attracting fixed point across an unstable fixed point in one-dimensional maps. The calculation starts from the trace formula for the eigenvalues of the Frobenius-Perron operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined from the loop formed by two heteroclinic orbits connecting back and forth the two fixed points of the one-dimensional map extended to a two-dimensional symplectic map. The escape rate is obtained with the expression of the prefactor to Arrhenius-van't Hoff exponential factor.