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The hydrodynamic part of the velocity autocorrelation function of a granularfluid in the homogeneous cooling state has been calculated by usingmode-coupling theory for a finite system with periodic boundary conditions. Theexistence of the shearing instability, leading to a divergent behavior of thevelocity flow fluctuations, is taken into account. A time region in which thevelocity autocorrelation function exhibits a power law decay, when time ismeasured by the number of collisions per particle, has been been identified.Also the explicit form of the exponential asymptotic long time decay has beenobtained. The theoretical prediction for the power law decay is compared withmolecular dynamics simulation results, and a good agreement is found, aftertaking into account finite size corrections. The effects of approaching theshearing instability are also explored.

Power-law decay of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state