Mode Coupling Theory for Small Scale

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(1) A simple toy modelA simple stochastic model consisting of two variables is discussed. An approximate solution is similar to that of MCT equation which satisfies the detailed balance as shown by Schmitz. If we generalize the number of variables as N (N>2), the approximate solution becomes an exact solution in the case of N->. It is a new purpose to understand qualitative differences between two-variable MCT and the generalized MCT after trying to obtain MCT given by Leutheusserand Goetze.(2) Dynamical Density Functional Theory :There are a lot of studies and researches to understand phenomena of microscopic scale which occur at the surface and interface of crystals on the basis of a concept of continuum. Recently this theory is understood to have tight relation with MCT can be applied to microscopic scale phenomena.