Research on glass transition, and its mechanism based on the density functional theory

作为密度泛函理论（DFT）的推广，我们建立了M体DFT，其中M是大于1的任意整数。M=2对应于超网链（HNC）理论。对于M=3，我们成功地进行了一维液体的数值计算。也就是说，经过大约10000次的迭代，相当复杂的积分方程给出了收敛解的两体和三体相关函数。作为密度泛函理论的动力学推广，我们应用Mori-Fujisaka投影算子方法导出了密度场几率泛函的Fokker-Planck方程。这个方程与我们十多年前导出的方程相同，但自由能泛函是基于微正则系综的，而与旧的基于巨正则系综的自由能泛函有很大的不同。对于玻璃化转变，我们进行了一种新的分子动力学模拟，其中一些粒子被固定在空间中（不允许移动）。这些固定粒子对稠密液体中的弛豫动力学有重要的影响，并由此得到了动力学关联区域大小的定量信息，最后给出了矩形盒中两粒子系统的精确解。我们讨论了这个简单系统的货车德瓦耳斯不稳定性和慢动力学解析。

As an extension of the density functional theory (DFT), we formulated M-body DFT with M an arbitrary integer larger than 1. M=2 corresponds to the hypernetted-chain (HNC) theory. For M=3 we successfully performed numerical calculations for one-dimensional liquids. That is, about after 10000 times of iteration, rather complicated integral equation gave converged solutions for two- and three-body correlation functions. And the results turned out to improve the HNC theory considerably.As a dynamic extension of the DFT, We applied the Mori-Fujisaka projection operator method to derive the Fokker-Planck equation for the probability functional of the density field. This equation is the same with the one already derived by us more than ten years ago but the free-energy functional is based on the microcanonical ensemble and it is quite different from the old one which is based on the grand canonical ensemble. The application of this new dynamic equation in the field of glass transition is now under consideration.As to the glass transition, we performed a new kind of molecular dynamics simulations, in which some particles are held fixed in space (not allowed to move). These fixed particles affect significantly on relaxation dynamics in dense liquids and from this we obtained quantitative information on the size of a dynamically correlated region.Finally we gave an exact solution to the two particle system confined in a rectangular box. We discussed the van der Waals instability and slow dynamics in this simple system analytically.