Time dependent correlations in a supercooled liquid from nonlinear fluctuating hydrodynamics

We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH) for the supercooled liquid. The time correlation of the density fluctuations in equilibrium obtained here shows quantitative agreement with molecular dynamics(MD) simulation data. We demonstrate numerically that the 1/rho nonlinearity in the NFH equations of motion is essential in restoring the ergodic behavior in the liquid. Under nonequilibrium conditions the time correlation functions relax in a manner similar to that observed in the molecular dynamics simulations in binary mixtures. The waiting time t_w dependence of the non-equilibrium response function follows a Modified Kohlrausch-Williams-Watts(MKWW) form similar to the behavior seen in dielectric relaxation data.