LARGE TIME OUT-OF-EQUILIBRIUM DYNAMICS OF A MANIFOLD IN A RANDOM POTENTIAL

We study the out-of-equilibrium dynamics of an elastic manifold in a r andom potential using mean-field theory. We find two asymptotic time r egimes: (i) stationary dynamics; (ii) slow aging dynamics with violati on of equilibrium theorems. We obtain an analytical solution valid for all large times with universal scalings of two-time quantities with s pace. A nonanalytic scaling function crosses over to ultrametricity wh en the correlations become long range. We propose procedures to test n umerically or experimentally the extent to which this scenario holds f or a given system.