Dynamical density functional approach to supercooled liquid and glass transition

Slow dynamics which shows up in supercooled liquid near the glass transition is discussed on the basis of the discretized version of the dynamical density functional equation which is the mesoscopic kinetic equation put forth recently in an attempt to go beyond the current mode-coupling theories. The discretization was realized through an appropriate mapping of the equation onto the kinetic lattice gas model in such a way that the master equation for the latter could approximately lead to the former upon coarse-graining of the spatio-temporal scales. The kinetic lattice gas model, which contains no ad hoc parameters except the direct correlation function of the reference liquid, is then solved for a hard-sphere liquid by using the ordinary Monte Carlo method to give successfully the thermally activated hopping process which is dominant at later times. Aspect of the free-energy landscape is also discussed.