Stochastic approach to glass transitions

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The main theme of the research project is to elucidate the dynamical properties of supercooled liquids near the glass transition, applying tlie trapping diffusion model to the stochastic dynamics of atoms seen in the supercooled liquids. We devised an efficient method to locate the glass transition point on the basis of the peak position of the non-Gaussian parameter. This method is powerful compared to the other methods, since the former uses only the informations at finite times. We used this method to fix the glass transition point for the soft-sphere liquid. In order to test the validity of the present model and compare the model with the softsphere system, we studied the waiting time distribution function and derived the explicit relation between the parameter in the model and the softsphere systems. We also studied the effect of the finite observation time. We showed that due to the subanomalous diffusion, the time required for the determination of physical quantities within a given accuracy increases before the glass transition point is reached. We also investigated the intermediate scattering function and the dynaurical structure factor and showed that the subanomalous regime of the trapping diffusion yields the characteristics of the alpha-relaxation, where the dynamical structure fac'Lor as a function of frequency decreases in a power-law form or the intermediate scattering function decreases stretched-exponentially in time.