Problems in Statistical Mechanics

在物理化学计划的这个项目中，凯斯将进一步发展液体的光散射理论，并研究非平衡统计力学的其他几个方面。这些项目包括发展输运动力学理论，在解析和计算机上研究生长模型和调幅分解，以及研究无序系统的光散射。在光散射理论和非平衡统计力学理论中，涉及高密度、大无序、大空间涨落等最困难的问题将受到攻击。这种强大的实空间重整化方法将直接应用于无序材料的光散射。无序系统的光散射不仅需要探测平均性质，而且实际上可能给出整个概率分布和新的信息，这一可能性将被研究。液体中的扩散理论将通过应用在上一笔赠款下开发的方法来推进。这些措施包括推导出一个应该准确描述液体的动力学方程，一种似乎非常适合于其解的变分方法，以及在动力学方程的求解中发展一个新的概念，找到求解该方程的随机计算机模拟。我们将寻求一种全新的方法来研究过冷液体中的输运理论，其基础是利用从力常数矩阵得到的量。在这一广泛研究范围内的其他几个项目也将继续进行。

In this project in the Physical Chemistry Program, Keyes will further develop the theory of light scattering from liquids and investigate several other aspects of nonequilibrium statistical mechanics. These projects include development of a kinetic theory of transport, studying growth models and spinodal decomposition both analytically and on the computer, and studying light scattering from disordered systems. In the theory of light scattering and in the theory of nonequilibrium statistical mechanics, the hardest problems, involving high density, large disorder, large spatial fluctuations, etc., will be attacked. The powerful method of real-space renormalization will be directly applied to light scattering from disordered materials. The possibility that light scattering from disordered systems need not probe averaged properties only, but may in fact give entire probability distributions and new information will be investigated. The theory of diffusion in liquids will be advanced via application of methods developed under the previous grant. These include the derivation of a kinetic equation which should describe liquids accurately, a variational method which seems well suited to its solution, and development of a new concept in the solution of kinetic equations, finding stochastic computer simulations which solve the equation. An entirely new approach to transport theory in supercooled liquids, based upon the utilization of quantities derived from the force constant matrix, will be pursued. Several other projects in this broad line of research also will be pursued.