Off-Equilibrium Glassy Dynamics: A Simple Case

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Abstract
We consider the relaxational dynamics of a particle in a random potential, taking into account the effects of a finite waiting time tw. In the limit of an embedding space of infinite dimension, we solve numerically the closed set of causal equations relating the correlation and response functions in the glass phase. The results at large waiting times agree with the static replica-symmetry-breaking approach and with previous studies of the equilibrium dynamics. For finite tw there may exist a hierarchical structure of crossover regimes between the measurement time and some functions of tw.