Strong clustering of non-interacting, passive sliders driven by a Kardar-Parisi-Zhang surface

TL;DR

This paper investigates the extreme clustering behavior of passive particles driven by a KPZ surface, revealing a robust Strong Clustering State through simulations and analytical results, applicable in both equilibrium and non-equilibrium regimes.

Contribution

It introduces the concept of Strong Clustering State for passive particles on KPZ surfaces and demonstrates its robustness and analytical characterization.

Findings

Particles exhibit extreme clustering in the Strong Clustering State.

The clustering is robust against changes in surface and particle update speeds.

Analytic results from the equilibrium Sinai model agree with non-equilibrium simulations.

Abstract

We study the clustering of passive, non-interacting particles moving under the influence of a fluctuating field and random noise, in one dimension. The fluctuating field in our case is provided by a surface governed by the Kardar-Parisi-Zhang (KPZ) equation and the sliding particles follow the local surface slope. As the KPZ equation can be mapped to the noisy Burgers equation, the problem translates to that of passive scalars in a Burgers fluid. We study the case of particles moving in the same direction as the surface, equivalent to advection in fluid language. Monte-Carlo simulations on a discrete lattice model reveal extreme clustering of the passive particles. The resulting Strong Clustering State is defined using the scaling properties of the two point density-density correlation function. Our simulations show that the state is robust against changing the ratio of update speeds of the surface and particles. In the equilibrium limit of a stationary surface and finite noise, one obtains the Sinai model for random walkers on a random landscape. In this limit, we obtain analytic results which allow closed form expressions to be found for the quantities of interest. Surprisingly, these results for the equilibrium problem show good agreement with the results in the non-equilibrium regime.