LARGE TIME NONEQUILIBRIUM DYNAMICS OF A PARTICLE IN A RANDOM-POTENTIAL

We study the nonequilibrium dynamics of a particle in a general N-dime nsional random potential when N --> infinity. We demonstrate the exist ence of two asymptotic time regimes: (i) stationary dynamics and (ii) slow aging dynamics with violation of equilibrium theorems. We derive the equations obeyed by the slowly varying part of the two-time correl ation and response functions and obtain an analytical solution of thes e equations. For short-range correlated potentials we find that (i) th e scaling function is nonanalytic at similar times and this behavior c rosses over to ultrametricity when the correlations become long range and (ii) aging dynamics persists in the limit of zero confining mass w ith universal features for widely separated times. We compare the nume rical solution to the dynamical equations and generalize the dynamical equations to finite N by extending the variational method to the dyna mics.