Nano-pattern stabilization by multiplicative noise

Abstract

Within the reaction--diffusion framework, a one-component system wasconfined by means of a multiplicative noise, into the attractionbasin of a patterning attractor in its (infinite-dimensional)configuration space. In this way, inhomogeneities that otherwisewould have been ``expelled" from this basin and subsequentlyeliminated through the diffusive process, were stabilized. For thepresent study, a model describing the physics of adsorbed particleson a metallic surface has been used. In particular, an underlyingdeterministic inhomogeneity-building mechanism was exploited, thatacts driven by lateral interactions among the adsorbed particles.This process cannot by itself sustain and stabilize theinhomogeneities, but together with the contribution of a particularform of multiplicative noise, it is able to confine the system intothe region of configuration space where this mechanism is enabled,hence stabilizing the pattern. Although the proposal could beapplied to more general situations, for the particular model studiedhere we have found that nanopatterns that without the indicatednoise source would be eliminated by diffusion, under its effect cangrow and be stabilized.