SPECTRAL PROPERTIES OF A TIME-PERIODIC FOKKER-PLANCK EQUATION

The Floquet spectrum of the time-periodic Fokker-Planck equation for a driven Brownian rotor is studied. We show that the Fokker-Planck equa tion can be transformed to a Schrodinger-like equation, with the same set of eigenvalues, whose dynamics is governed by a time-periodic Hami ltonian in which the diffusion coefficient plays a role analogous to P lanck's constant. For a small diffusion coefficient, numerical calcula tions of the spectrum starting from the Schrodinger-like equation are more convergent than those starting from the Fokker-Planck equation. W hen the Hamiltonian exhibits a transition to chaos, those decay rates affected by the chaotic regime exhibit level repulsion. This level rep ulsion of decay rates, in turn, changes the behavior of a typical mean first passage time in the problem. The size of the diffusion coeffici ent determines the extent to which the stochastic dynamics is affected by the transition to chaos in the underlying Hamiltonian.