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

Unified description on the long-time tail of velocity autocorrelation function (VACF) and the algebraic decays of the equal-time spatial correlation functions for nearly elastic and uniformly sheared granular liquids is developed based on the generalized fluctuating hydrodynamics. We predict that the crossover of the long-time tail of VACF from t(-3/2) to t(-5/2) with the time t regardless of the density. We also demonstrate the existence of algebraic tails of the equal-time spatial density correlation function and the equal-time spatial velocity correlation function which respectively satisfy r(-11/3) and r(-5/3) for large distance r.