Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems.

Abstract

I show that nonequilibrium two-dimensional interfaces between three-dimensional phase separated fluids exhibit a peculiar "sublogarithmic" roughness. Specifically, an interface of lateral extent L will fluctuate vertically (i.e., normal to the mean surface orientation) a typical rms distance w≡sqrt[〈|h(r,t)|^{2}〉]∝[ln(L/a)]^{1/3} [where a is a microscopic length, and h(r,t) is the height of the interface at two-dimensional position r at time t]. In contrast, the roughness of equilibrium two-dimensional interfaces between three-dimensional fluids, obeys w∝[ln(L/a)]^{1/2}. The exponent 1/3 for the active case is exact. In addition, the characteristic timescales τ(L) in the active case scale according to τ(L)∝L^{3}[ln(L/a)]^{1/3}, in contrast to the simple τ(L)∝L^{3} scaling found in equilibrium systems with conserved densities and no fluid flow.