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
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.
PACS: 05.70.Ln – Non equilibrium and irreversible thermodynamics / 64.70.Pf – Glass transitions / 75.10.Nr – Spin-glass and other random models / 83.50.Gd – Nonlinear viscoelasticity
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001