Research on glass transition, and its mechanism based on the density functional theory

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As an extension of the density functional theory (DFT), we formulated M-body DFT with M an arbitrary integer larger than 1. M=2 corresponds to the hypernetted-chain (HNC) theory. For M=3 we successfully performed numerical calculations for one-dimensional liquids. That is, about after 10000 times of iteration, rather complicated integral equation gave converged solutions for two- and three-body correlation functions. And the results turned out to improve the HNC theory considerably.As a dynamic extension of the DFT, We applied the Mori-Fujisaka projection operator method to derive the Fokker-Planck equation for the probability functional of the density field. This equation is the same with the one already derived by us more than ten years ago but the free-energy functional is based on the microcanonical ensemble and it is quite different from the old one which is based on the grand canonical ensemble. The application of this new dynamic equation in the field of glass transition is now under consideration.As to the glass transition, we performed a new kind of molecular dynamics simulations, in which some particles are held fixed in space (not allowed to move). These fixed particles affect significantly on relaxation dynamics in dense liquids and from this we obtained quantitative information on the size of a dynamically correlated region.Finally we gave an exact solution to the two particle system confined in a rectangular box. We discussed the van der Waals instability and slow dynamics in this simple system analytically.