Aging and non-linear glassy dynamics in a mean field model |
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Authors: | F Thalmann |
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Institution: | (1) LEPES-CNRS, Laboratoire associéà l'UJF-Grenoble, BP166X, 25 avenue des Martyrs, 38042 Grenoble Cedex, France aaand Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK, GB |
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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 v∼F
4, 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.
Received 7 May 2000 and Received in final form 22 August 2000 |
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Keywords: | 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 |
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