Problems in Statistical Mechanics

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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.