Gaussian density fluctuations, mode coupling theory and all thatG. Szamel
Department of Chemistry, Colorado State University - Ft. Collins, CO 80523, USA
(Received 14 October 2003; accepted in final form 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.
61.20.Lc - Time-dependent properties; relaxation.
64.70.Pf - Glass transitions.
61.20.Gy - Theory and models of liquid structure.
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