Fluctuation-Dissipation Relations for Motions of Center of Mass in Driven Granular Fluids under Gravity

Details Fluctuation-Dissipation Relations for Motions of Center of Mass in Driven Granular Fluids under Gravity Fluctuation-Dissipation Relations for Motions of Center of Mass in Driven Granular Fluids under Gravity

2012-02-10

arxiv.org/abs/1202.2224v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, LaTeX, 12 figures

Scientific paper

We investigate a validity of fluctuation-dissipation relations in a nonequilibrium stationary state of fluidized granular media under gravity. A phenomenological Langevin-type theory describing the fluctuation of center of mass height, which was originally constructed for one-dimensional granular gas on a vibrating bottom plate, is generalized to any dimensions even for the case that the vibrating bottom plate is replaced by a thermal wall. The theory gives analytical expressions for the power spectrum and response function of the center of mass height; furthermore, it predicts a fluctuationdissipation relation between them, which is known to be satisfied at equilibrium, with a modification that equilibrium temperature is replaced by an effective temperature defined by a kinetic energy of the center of mass. To check these explicit theoretical predictions, we performed extensive and accurate event-driven molecular dynamics simulations for the model system with a thermal wall at the bottom. We found that the power spectrum and response function of the center of mass height show good agreement with theoretical predictions within a range of time scales in which our theory is valid. As the most remarkable result, it is shown that a fluctuation-dissipation relation for the granular system is well satisfied especially at a large frequency (short time) region in a wide range of system parameter. We finally remark that the relation between systematic deviations at a small frequency (long time) region and time scales of the driven granular system.

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