Trace formula for activated escape in noisy maps

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.