The discoveries of slowness

Theoretical progresses in off-equilibrium behavior of glassy systems

  • Giorgio Parisi
  • 09 / 2011 Seite: 29

Many systems approach equilibrium very slowly. Their equilibration time becomes macroscopic and is sometimes so large that it cannot be measured. Significant progress have recently been made in understanding the collective phenomena that are at the basis of this behavior, especially in structural glasses and spin glasses.

The typical microscopic time scale in condensed matter physics is the picosecond. However sometimes the time to approach equilibrium is much larger (e. g. seconds, years ....). When the gap between the microscopic and the macroscopic time becomes very large, the most common scenarios are the following:
- There is a localized microscopic process with large activation energy that is responsible for the very large equilibration time.
- All the localized microscopic processes are fast: there is no single very large energy barrier and the very slow behavior is a collective effect.

The most well understood collective effects happen at a second order phase transition point where there are large-scale excitations that involve a large number of atoms. At the phase transition point the spatial correlation length diverges and at the same time scale becomes very large (critical slowing down): in this situation the characteristic times are much larger than the microscopic time, but usually they still remain microscopic (e. g. they diverge at the critical temperature Tc as |T–Tc|–1.4 with a prefactor that is of order of the microscopic time scale). ...

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