Brownian motion with "green" noise in a periodic potential

The motion of a Brownian particle in a periodic potential is considered provided that the external force is a high-pass filtered ("green") noise. In this case the spectrum of the noise has no constant component, and the diffusion coefficient of the Fokker-Planck equation is zero. Therefore, the Krylov-Bogoliuboff averaging method is employed. It is shown that green noise does not destroy the locking state of the stochastic system under study. The life time of this state is estimated; and the dependence of a lock-in bandwidth on the statistical properties of noise is found. A ring laser is considered as an example. (C) 1998 Published by Elsevier Science B.V.