Clustering, intermittency and scaling for passive particles on fluctuating surfaces

Abstract

We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for passive particles sliding on one-dimensional Edwards-Wilkinson or Kardar-Parisi-Zhang surfaces, with particles moving either along or against the growth direction in the latter case. Extensive numerical simulations are supplemented by analytical results for a sticky slider model in which particles coalesce when they meet. Results for single particle displacement versus time show to what extent particle dynamics is slaved to the surface, while scaling properties of the probability distribution of the separation of two particles have important implications for replica symmetry breaking for a pair of trajectories. For the many-particle system, clustering in steady state is studied via moments of particle number fluctuations in a single stretch, revealing different degrees of spatial multiscaling with different driving. Temporal intermittency in steady state is established by showing that the scaled flatness diverges. Finally we consider the approach to the steady state, and study both the flatness and the evolution of equal-time correlation functions, as in coarsening of phase ordering systems. Our studies give clear evidence for a simple scaling description of the approach to steady state, with a diverging length scale. An investigation of aging properties reveals that flatness is nonmonotonic in time with two distinct branches, and that a scaling description holds for each one.