Out of equilibrium dynamics: an overview
Giulio Biroli
Abstract
There are very different physical situations
for which the keyword "out of equilibrium dynamics"
is used. Roughly one can consider 3 different classes:
- Metastability. Example:
a liquid can exist below its freezing point. When this happens
we say that the liquid is supercooled. This is a metastable
state in which the system is clearly out of equilibrium.
- Driven systems.
Some power is continuously injected into the system which
therefore remains in a stationary out of equilibrium state.
Example: fully developed turbulence, motion of vortex lines in
a superconductor.
- Slow relaxation and glassy dynamics.
The evolution of a system coupled to a thermal bath
and starting from an out of equilibrium initial condition
does not always end up in equilibrium. Many systems remain always
out of equilibrium!
Example: A ferromagnet, a spin glass, a glass, ...
quenched from a temperature well above Tc to a temperature
well below Tc (Tc is the phase transition temperature).
This talk will give an overview of what is known, accepted and debated
on the problem of slow relaxation and glassy dynamics (for classical
systems).
After an introduction to the experimental results, I shall introduce
the two main theoretical approaches to the problem, namely scaling theory
and mean field (or mode-coupling) theory and I will discuss the main
physical predictions of these two methods. The emphasis will be put on
concepts and principles. However, to give a flavor of the two theoretical
approaches the case of domain growth or coarsening will be worked out
completely.
References
A good and recent review on "out of equilibrium dynamics
in spin-glasses and other glassy sustems" is
J.P. Bouchaud, L.F. Cugliandolo, J. Kurchan and M. Mezard,
in "Spin Glasses and Random Fields", A.P. Young Editor,
World Scientific; also avalaible on condmat/9702070.
A good review on "Domain Growth and
Coarsening" is: A.J. Bray, Adv. in Phys. V43 (1994) 357
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Original papers on scaling theory for out of equilibrium dynamics are:
-for the Random Field Ising Model: J. Villain, PRL V52 (1984) 1543
-Spin Glasses: D.S. Fisher and D. Huse, PRL V56 (1986) 1601 and
PRB V38 (1988) 373
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The original paper on the mean field theory for out of equilibrium
dynamics is:
-L.F. Cugliandolo and J. Kurchan, PRL V71 (1993) 173; Phil. Mag. B V71
(1995) 501
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A nice example of a phenomenological theory of the out of equilibrium
dynamics and a discussion of the concept of "weak ergodicity breaking"
can be found in:
J.P. Bouchaud, J. Phys. France V2 (1992) 1705