Slow dynamics of equilibrium density fluctuations in suspensions of colloidal hard spheres near the glass transition

A mean-field theory for the dynamics of equilibrium suspensions of colloida l hard spheres near the glass transition is presented based on the standpoi nt recently proposed by the present author. It is shown that although the r elative magnitude of the density fluctuations to the mean equilibrium densi ty is small even near the glass transition, they are described by a nonline ar stochastic equation which originates from the long-range hydrodynamic in teractions between particles. A nonlinear mean-field equation for the parti cle mean-square displacement is then derived. This equation is used to anal yze the recent experimental data for equilibrium colloidal suspensions. Ana lyses show that no divergence of the alpha- and beta -relaxation times is f ound in the experimental data, although the dynamic properties of the collo idal liquid exhibit a drastic slowing down in the so-called supercooled reg ion.