Stochastic manifestation of chaos in a Fokker-Planck equation

We have studied the behavior of the Floquet spectrum for A Fokker-Planck equation describing a nonlinear Brownian rotor driven by an angle-dependent dynamic external force consisting of two traveling sine waves with amplitudes ${\epsilon }_1$ and ${\epsilon }_2$. For the case ${\epsilon }_2$=0, the Fokker-Planck equation is separable (in the sense that is has two well defined eigen-numbers) and the nearest-neighbor spacing distribution appears to be Poisson random for small spacings. For both ${\epsilon }_1$≠0 and ${\epsilon }_2$≠0, we observed nonlinear resonance and level repulsion, indicating that the spectrum, at least locally, exhibits universal random-matrix-type behavior and that information about the underlying dynamics of the Brownian particle is lost from the spectrum.