Eur. Phys. J. B 19, 65-73 (2001)
https://doi.org/10.1007/s100510170350

Aging and non-linear glassy dynamics in a mean field model

LEPES-CNRS, Laboratoire associé à l'UJF-Grenoble, BP166X, 25 avenue des Martyrs, 38042 Grenoble Cedex, France and Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

Corresponding author: ^a fabrice@theory.ph.man.ac.uk

Received: 7 May 2000
Revised: 22 August 2000
Published online: 15 January 2001

Abstract

The mean field approach of glassy dynamics successfully describes systems which are out-of-equilibrium in their low temperature phase. In some cases an aging behaviour is found, with no stationary regime ever reached. In the presence of dissipative forces however, the dynamics is indeed stationary, but still out-of-equilibrium, as inferred by a significant violation of the fluctuation dissipation theorem. The mean field dynamics of a particle in a random but short-range correlated environment, offers the opportunity of observing both the aging and driven stationary regimes. Using a geometrical approach previously introduced by the author, we study here the relation between these two situations, in the pure relaxational limit, i.e. the zero temperature case. In the stationary regime, the velocity (v)-force (F) characteristics is a power law , while the characteristic times scale like powers of v, in agreement with an early proposal by Horner. The cross-over between the aging, linear-response regime and the non-linear stationary regime is smooth, and we propose a parametrization of the correlation functions valid in both cases, by means of an "effective time". We conclude that aging and non-linear response are dual manifestations of a single out-of-equilibrium state, which might be a generic situation.