Local fluctuations in the non-equilibrium dynamics of a Lennard-Jones glass

We investigate local fluctuations in the out of equilibrium dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to the glass state. Motivated by recent experiments that probe fluctuations in glassy materials at distance scales of the order of tens of nanometers, we define the local (i.e. averaged over a small region in the sample) two-time mean square displacement Delta(r) (t, t(w)) and two-time intermediate scattering function C-r(t, t(w)). We study the probability distributions for the values of these local two-time functions as a function of both time variables. We discuss the connection between the scaling behavior of the probability distributions and a soft mode controlling the slow dynamics.