Monte Carlo Simulation of the Dynamical Density Functional Equation for Supercooled Liquids
Monte Carlo Simulation of the Dynamical Density Functional Equation for Supercooled Liquids
复制标题
过冷液体动力密度泛函方程的蒙特卡罗模拟
DOI：
10.1143/ptps.126.305
复制
发表时间：
1997
影响因子：
--
通讯作者：
S. Miyazima
中科院分区：
文献类型：
--
作者：
K. Kawasaki;K. Fuchizaki;S. Miyazima
动力学密度泛函理论（DDFT）在参考文献1）和引用的参考文献中描述的是最自然的方程，它体现了这样一种思想，即在足够稠密的流体中，密度是描述局部小尺度运动的唯一慢变量。从这个观点来看，最近的模拟，模拟朗之万方程3）包含动量和密度变量在相对较短的时间，然后切换到蒙特卡洛模拟4l，使用Ramakrishnan-Yussouff型密度泛函5l作为能量在较长的时间是不太令人满意的研究过冷稠密液体中的玻璃态慢动力学。在我们的DDFT方法中，我们在一开始就解析地消除了快速变化的动量变量，并获得了一个封闭的随机方程，只包含密度变量。这个单一的动力学方程包括模式耦合理论（MCT）的非线性反馈机制，6）并且同时允许长时间模拟大幅度密度波动。7），*）因此，我们的DDFT是Cohen和de Schepper 8）直观思想的自然体现，即在稠密流体中，只有密度变量是控制短距离行为的缓慢变化的总变量。9），**）此外，我们能够将我们的方程映射到一种自旋交换动力学伊辛模型，从而可以通过标准Monte Carlo模拟方法进行研究。我们在参考文献7）中已经表明，我们的DDFT方程可以映射到动力学伊辛模型上，在该模型中，属于最近邻粗粒化单元的任何一对自旋之间以相等的概率发生自旋交换。进入伊辛模型的能量表示为Eo（n），
The dynamical density functional theory (DDFT) described in Ref. 1) and the references quoted therein is the most natural equation that embodies the idea that in sufficiently dense fluids the density is the only slow variable that describes local small scale motions. From this point of view, the recent simulations that simulate the Langevin equation 3) containing the momentum and density variables at relatively short times and then switch to the Monte Carlo simulation 4l which uses the Ramakrishnan-Yussouff type density functional 5l as the energy at longer times are not quite satisfactory for studying glassy slow dynamics in supercooled dense liquids. In our DDFT approach we at the outset analytically eliminate the momentum variable which varies rapidly and obtain a closed stochastic equation containing only the density variable. This single dynamical equation includes the nonlinear feedback mechanism of the mode coupling theory (MCT), 6) and at the same time permits long time simulation with large amplitude density fluctuations. 7),*) Thus our DDFT is a natural embodiment of the intuitive idea of Cohen and de Schepper 8) that in dense fluids only the density variable is the slowly-varying gross variable governing the short distance behavior. 9),**) Furthermore, we are able to map our equation onto a kind of spin-exchange kinetic Ising model, which can thus be studied by the standard Monte Carlo simulation method. We have shown in Ref. 7) that our DDFT equation can be mapped onto the kinetic Ising model where spin exchanges take place with equal probability between any pair of spins belonging to the nearest neighbor coarse graining cells. The energy entering the Ising model denoted as Eo ( n) is