Slow dynamics in condensed matter: spinodal decomposition and glass transition

A brief review is presented about our recent work on computer studies of a continuum model describing spinodal decomposition of binary fluid, which quantitatively accounts for corresponding experimental results. We then switch over to discussing problems of glass transitions. First we consider the ultraslow mode observed in fragile glass-formers, where the diffusive behavior of this mode is explained in terms of phase dynamics describing slow relaxation of spatial heterogeneous structure resulting from spontaneous break-down of continuous translational symmetry. Next we present a stochastic model for density fluctuation in supercooled liquids, which is mapped onto a certain kinetic lattice gas model which is convenient for Monte Carlo simulation studies.