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Anomalous Collective Diffusion in One-dimensional Driven Granular Media

We numerically investigate the nonequilibrium steady state of a one-dimensional rarefied granular system in which each particle is driven by Gaussian white noise and subject to inelastic mutual collisions. We find that the dynamic structure factor S ( q , t ) decays as exp (- D q 2 t 2 ), which is in marked contrast to the usual Fickian behavior exp (- D q 2 t ). Employing newly obtained S ( q , t ), we demonstrate that the static spatial correlation function and the one-point time correlation function obey the same scaling behavior.