Nonlinear density fluctuations and spatial heterogeneities near the colloidal glass transition

How the spatial heterogeneities play an important role in the dynamics of density fluctuations near the colloidal glass transition is discussed from a new viewpoint. A nonlinear stochastic diffusion equation for the density fluctuations recently proposed by one of the present authors (MT) is numerically solved in two different initial states, an equilibrium state and a nonequilibrium state. Depending on initial states, the dynamics of the spatial heterogeneities are shown to be quite different from each other. Such differences are thus shown to influence the slow relaxations of density fluctuations, leading to different types of two-step relaxations.