Volume 65, Number 4, February 2004
|Page(s)||498 - 504|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 February 2004|
Gaussian density fluctuations, mode coupling theory and all that
Department of Chemistry, Colorado State University - Ft. Collins, CO 80523, USA
Accepted: 5 December 2003
We consider a toy model for glassy dynamics of colloidal suspensions: a single Brownian particle diffusing among immobile obstacles. If Gaussian factorization of static density fluctuations is assumed, this model can be solved without factorization approximation for any dynamic correlation function. The solution differs from that obtained from the ideal mode coupling theory (MCT). The latter is equivalent to including only some positive-definite terms in an expression for the memory function. An approximate re-summation of the complete expression suggests that, under the assumption of Gaussian factorization of static fluctuations, mobile particle's motion is always diffusive. In contrast, MCT predicts that the mobile particle becomes localized at a high enough obstacle density. We discuss the implications of these results for models for glassy dynamics.
PACS: 61.20.Lc – Time-dependent properties; relaxation / 64.70.Pf – Glass transitions / 61.20.Gy – Theory and models of liquid structure
© EDP Sciences, 2004
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