Pico-canonical ensembles: A theoretical description of metastable states

Abstract

We define restricted ensembles, called pico-canonical ensembles, for a statistical-mechanical description of the metastable and glassy phases. In this approach, time-evolution is Markovian, with temperature dependent rates. Below a particular glass-temperature, the system is strongly non-ergodic, and the phase space breaks up into a large number of mutually disconnected sectors. Averages are calculated over states within one such sector, and then averaged over sectors. As a soluble example, we calculate these explicitly for a one dimensional lattice gas with nearest neighbor couplings.

13 pages, latex, 1 figure, text of invited talk delivered at at the conference on 'Slow Dynamical Processes in Nature', Seoul, Nov.25-27,2001

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