Unified description of long-time tails and long-range correlation functions for sheared granular liquids

Abstract. Unified description on the long-time tail of velocity autocorrelation function and the longrange correlation for the equal-time spatial correlation functions is developed based on the generalized fluctuating hydrodynamics. The cross-over of the long-time tail from t to t is predicted independent of the density, and the equal-time spatial density correlation function and the equal-time spatial velocity correlation function respectively satisfy r and r for large r limit.