Statistical Physics of Structural Glass

基于第一性原理的玻璃化转变的模式耦合理论(MCT)已经成功地解释了许多实验结果，并在最近受到了广泛的关注。然而，所使用的激烈近似的性质尚不清楚。揭示这个问题的一种方法是彻底设计出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在2003年开始的系统展开方法很难违反涨落-耗散关系，尽管标准的MCT方程被恢复到最低阶。使用BiRoli等人的改进版本的场论，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)]。这一新理论重现了标准MCP的单圈有序，使系统的高阶计算成为可能。一个密切相关的方法是动力学密度泛函理论(DDFT)，它原则上可以考虑标准MCT中不同的热激活过程。最近，我们利用一种新的投影算子方法对DDFT的两个版本，即完全确定版本和随机版本进行了内插。

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.