AC-driven Brownian motors: A Fokker-Planck treatment

We consider a model of AC-driven Brownian motors consisting of a classical particle which is placed in a potential that is periodic in space and time and which is coupled to a heat bath. The effects of fluctuations and dissipation are studied by a time-dependent Fokker-Planck equation. The approach lets us map the original stochastic problem onto a system of ordinary linear algebraic equations. The solution of the equations provides complete information about ratchet transport, avoiding the disadvantages of direct stochastic calculations such as long transients and large statistical fluctuations. The Fokker-Planck approach to dynamical ratchets opens the possibility for further generalizations.