STOCHASTIC LANDAU EQUATION WITH TIME-DEPENDENT DRIFT

The stochastic differential equation tau-0-partial-t A = epsilon(t) A - g3 A3 + f(t)BAR, where f(t)Bar is Gaussian white noise, is studied for arbitrary time dependence of epsilon(t). In particular, cases are considered where epsilon(t) goes through the bifurcation of the deterministic system, which occurs at epsilon = 0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P (A,t). The results compare favorably with a numerical simulation of the stochatic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of epsilon(t). The procedure can be generalized to an arbitrary deterministic part partial-t A = D (A,t) + fBAR(t), but the deterministic equation may then have to be solved numerically.