Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

Details Passive Sliders on Fluctuating Surfaces: Strong-Clustering States Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

2005-05-11

arxiv.org/abs/cond-mat/0505292v1

Phys. Rev. Lett. 94, 240601 (2005)

Physics

Condensed Matter

Statistical Mechanics

To be published in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.94.240601

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.

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