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 and the long-range 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 $t^{-3/2}$ to $t^{-5/2}$ is predicted independent of the density, and the equal-time spatial density correlation function and the equal-time spatial velocity correlation function respectively satisfy $r^{-11/3}$ and $r^{-5/3}$ for large $r$ limit.