Stochastic manifestation of chaos

We use Floquet theory to study the dynamical properties of a Fokker-Planck equation with time-dependent coefficients describing a nonlinear Brownian rotor driven by a time-periodic angle-dependent 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 it has two well-defined eigen-numbers), and the nearest-neighbor spacing distribution appears to be Poisson random for large ${\epsilon }_1$. For both ${\epsilon }_1$≠0 and ${\epsilon }_2$≠0, we find evidence of nonlinear resonance and level repulsion in the Floquet spectrum and first-passage time, and the spectrum exhibits level repulsion and universal random matrix-type behavior. The long-time state is quasiperiodic in time and angle and is affected by an increasing number of modes of the system as the external field amplitude is increased.