Nonequilibrium dynamics of a supercooled liquid using schematic and structural models

The glassy aging data of dielectric relaxation fits to a modified Kohlrausch-Williams-Watts (MKWW) form exp−tage/τageβage. The relaxation time τage(tage) and the stretching exponent βage are both independent of the frequency of the corresponding data. We discuss two theoretical models to study this non equilibrium dynamics. First we discuss a schematic soft-spin model in which the aging behavior follows the MKWW form similar to the above dielectric data. The nature of the modified fluctuation-dissipation relation (FDR) is also studied in the time as well as correlation windows. Second, we solve numerically the equations of fluctuating nonlinear hydrodynamics (FNH) generalized to short wave lengths for a simple Lennard-Jones liquid. The correlation of density fluctuations at two and four points level are studied using the same density fluctuation data. The respective equilibration of both two point and four point functions follow the MKWW form with relaxation times (dependent of tage) which are very different in the two cases.