Journal of Statistical Physics, Vol. 93, Nos. 5/6, 1998 Received February 3, 1998; final July 28, 1998 We consider a Ginzburg–Landau equation in the interval [—e~\ e" 1 ], e>0, with Neumann boundary conditions, perturbed by an additive white noise of strength ^fl, and reaction term being the derivative of a function which has two equal–depth wells at ±1, but is not symmetric. When « = 0, the equation has equilibrium solutions that are increasing, and connect —1 with +1. We call them instantons, and we study the evolution of the solutions of the perturbed equation in the limit s -* 0 + , when the initial datum is close to an instanton. We prove that, for times that may be of the order of e~\ the solution stays close to some instanton whose center, suitably normalized, converges to a Brownian motion plus a drift. This drift is known to be zero in the symmetric case, and, using a perturbative analysis, we show that if the nonsymmetric part of the reac- tion term is sufficiently small, it determines the sign of the drift. KEY WORDS: Stochastic PDEs; interface dynamics; infinite-dimensional processes. Interface Fluctuations for the D = 1 Stochastic Ginzburg–Landau Equation with Nonsymmetric Reaction Term Stella Brassesco 1 and Paolo Butta 2 INTRODUCTION We consider a stochastic perturbation of the one dimensional Ginzburg– Landau (G–L) equation with Neumann boundary conditions (N.b.c.) in the interval [—£"', £"'], where £ is a parameter that will go to zero. The potential term is a double well function V with equal minima at +1, and the stochastic perturbation is given by a space time white noise, with inten- sity s /e. The two minima of the potential give rise to two equilibrium 1 Instituto Venezolano de Investigaciones Cientificas, Caracas 1020-A, Venezuela; e-mail: sbrasses@ivic.ivic.ve. 2 Center for Mathematical Sciences Research, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854-8019; e-mail: pbutta@math.rutgers.edu. 1111 0022-4715/98/1200-1111$15.00/0 © 1998 Plenum Publishing Corporation