Gaussian density fluctuations , mode coupling theory , and all that

– 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. Introduction. – During the last decade considerable effort has been devoted to simula-tional and experimental verification of the mode coupling theory (MCT) of glassy dynamics and the glass transition [1–3]. The consensus that emerged from this work is that MCT describes in a satisfactory way " weakly " supercooled liquids (i.e. it describes the first few decades of slowing down on approaching the glass transition). In particular, MCT has been quite successful when applied to concentrated colloidal suspensions [4], the colloidal glass [5], and gelation [6] transitions. Notably, less effort has been devoted to the foundations of the mode coupling theory (see, however, Refs. [7–9]). This is somewhat surprising in view of MCT's several well-known problems. The most important, fundamental problem is the uncontrolled nature of the basic MCT approximation: factorization of a complicated time-dependent pair-density (i.e. four-particle) correlation function. Recently, we proposed an extension of MCT for dynamics of colloidal suspensions and the colloidal glass transition [10]. Our theory includes, in an approximate way, time-dependent pair-density fluctuations. It relies upon a factorization approximation that is similar to that used in MCT, but is applied at a level of a memory function for the time-dependent pair-density correlation function. The theory predicts an ergodicity breaking transition similar to that of MCT, but at a higher density. Thus it partially solves another well-known MCT problem: overestimation of so-called dynamic feedback effect and the resulting underestimation of the colloidal glass transition density.