Renormalized diffusion in systems with periodic variables

The well-known results for the effective or renormalized diffusion of a Brownian particle in a periodic potential is generalized for arbitrary systems subject to Fokker-Planck equations with coefficients that are time-independent, periodic in at least one variable and such that no average motion persists. In presence of a bare diffusion the conservative and the dissipative drifts play a different role, and the renormalizing term results from the time integral of a combination of auto- and cross-correlations of both drifts. Nevertheless, the numerical evaluation of the result is essentially limited to solving the homogeneous and time-independent forward and backward equation within one period.Work supported by the Swiss National Science Foundation