Statistical Physics of Structural Glass

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The mode coupling theory (MCT) of glass transition based on first principles has succeeded in explaining a number of experimental findings and is receiving lots of attention lately. However, nature of the drastic approximations employed is unclear. One way to shed light on this problem is to work out thoroughly a simple toy model which captures some features of reality [Kim and Kawasaki, (2005)]. On the other hand, a systematic expansion approach started by Kawasaki in 2003 has a difficulty of violating the fluctuation-dissipation relation although the standard MCT equation was recovered in the lowest order. Using the improved version of the field theory due to Biroli et al, Kim and Kawasaki succeeded in avoiding this difficulty and in developing satisfactory field-theoretic approach [Kim and Kawasaki (2007, 2008)]. This new theory reproduces the standard MCP in the one-loop order and enables systematic higher order calculations.A closely related approach is the dynamical density functional theory (DDFT) which can in principle take into account the thermally activated processes abosent in the standard MCT. We recently interpolated two versions of DDFT, that is, fully deterministic one and stochastic version, by employing a new projection operator method.