Large times off-equilibrium dynamics of a particle in a random potential

Details Large times off-equilibrium dynamics of a particle in a random potential Large times off-equilibrium dynamics of a particle in a random potential

1995-05-24

arxiv.org/abs/cond-mat/9505112v1

Phys. Rev. E {\bf 53}, 1525 (1996)

Physics

Condensed Matter

70 pages, 7 figures included, uuencoded Z-compressed .tar file

Scientific paper

10.1103/PhysRevE.53.1525

We study the off-equilibrium dynamics of a particle in a general $N$-dimensional random potential when $N \to \infty$. We demonstrate the existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it ii.} slow aging dynamics with violation of equilibrium theorems. We derive the equations obeyed by the slowly varying part of the two-times correlation and response functions and obtain an analytical solution of these equations. For short-range correlated potentials we find that: {\it i.} the scaling function is non analytic at similar times and this behaviour crosses over to ultrametricity when the correlations become long range, {\it ii.} aging dynamics persists in the limit of zero confining mass with universal features for widely separated times. We compare with the numerical solution to the dynamical equations and generalize the dynamical equations to finite $N$ by extending the variational method to the dynamics.

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