Statistical Physics of Structural Glass

基于第一性原理的玻璃化转变模态耦合理论（MCT）成功地解释了许多实验结果，近年来受到广泛关注。然而，所采用的极端近似的性质尚不清楚。阐明这一问题的一种方法是建立一个简单的玩具模型，它能捕捉到现实的一些特征[Kim和Kawasaki，（2005）]。另一方面，Kawasaki于2003年开始的系统展开方法虽然在最低阶恢复了标准MCT方程，但难以违反涨落-耗散关系。利用Biroli等人提出的场论改进版本，Kim和Kawasaki成功地避免了这一困难，并发展了令人满意的场论方法[Kim和Kawasaki(2007, 2008)]。这一新理论再现了单环顺序的标准MCP，并使系统的高阶计算成为可能。一个密切相关的方法是动态密度泛函理论（DDFT），它原则上可以考虑标准MCT中没有的热激活过程。最近，我们采用一种新的投影算子方法插值了两个版本的DDFT，即完全确定性版本和随机版本。

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.