Colored noise and bistable Fokker-Planck equations

Abstract

The detailed dependence of the smallest nonzero eigenvalue of a bistable periodic Fokker-Planck equation on the external-noise correlation time is determined for the first time numerically to tie down contrasting theoretical predictions. The isospectrality with the Fokker-Planck equation for the metastable system defined by inversion of the bistable potential is proved analytically. This amounts to a generalized supersymmetric transformation between the corresponding non-Hermitean Hamiltonian operators.