Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

Apoorva Nagar 1, Mustansir Barma 1, Satya N. Majumdar 2

Physical Review Letters 94 (2005) 240601

We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a discrete version of the problem in one dimension reveal that particles cluster very strongly: the two point density correlation function scales with the system size with a scaling function which diverges at small argument. Analytic results are obtained for the Sinai problem of random walkers in a quenched random landscape. This equilibrium system too has a singular scaling function which agrees remarkably with that for advected particles.

  • 1. Department of Theoretical Physics,
    Tata institute of Fundamental Research
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud