Exact solutions of some urn models of relaxation in glassy dynamics

We consider two simple models, called "urn models," for a general N-ball, M-urn problem. These models find applications in the study of relaxation in glassy dynamics. We obtain exact analytical results in these two cases for the average relaxation time tau to reach the ground state. In mod...

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Bibliographic Details
Published in:Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999-07, Vol.60 (1), p.145-148
Main Authors: Arora, D, Bhatia, D P, Prasad, M A
Format: Article
Language:English
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Summary:We consider two simple models, called "urn models," for a general N-ball, M-urn problem. These models find applications in the study of relaxation in glassy dynamics. We obtain exact analytical results in these two cases for the average relaxation time tau to reach the ground state. In model I we also obtain the functional dependence of tau for large N, and in model II we obtain an asymptotic (N-->infinity) dependence of tau as a function of the number of urns M.
ISSN:1063-651X
1095-3787
DOI:10.1103/PhysRevE.60.145