Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium

By means of molecular dynamics computer simulations we investigate the out of equilibrium relaxation dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to low temperatures. We find that one-time quantities, such as the energy or the structure factor, show only a weak time dependence. By comparing the out of equilibrium structure factor with equilibrium data we find evidence that during the aging process the system remains in that part of phase space that mode-coupling theory classifies as liquid like. Two-times correlation functions show a strong time and waiting time t(w) dependence. For large t(w) and times corresponding to the early p-relaxation regime the correlators approach the Edwards-Anderson value by means of a power-law in time. For large but fixed values of t(w) the relaxation dynamics in the beta-relaxation regime seems to be independent of the observable and temperature. The a-relaxation shows a power-law dependence on time with an exponent which is independent of t(w) but depends on the observable. We find that at long times tau the correlation functions can be expressed as C-AG (h(t(w) + 7)/h(t(w))) and compute the function h(t). This function is found to show a t-dependence which is a bit stronger than a logarithm and to depend on the observable considered. If the system is quenched to very low temperatures the relaxation dynamics at long times shows fast drops as a function of time. We relate these drops to relatively local rearrangements in which part of the sample relaxes its stress by a collective motion of 50-100 particles. Finally we discuss our measurements of the time dependent response function. We find that at long times the correlation functions and the response are not related by the usual fluctuation dissipation theorem but that this relation is similar to the one found for spin glasses with one step replica symmetry breaking.