Metastable state dynamics and power law relaxation in a supercooled liquid

We consider glassy relaxation by using a model for supercooled liquid where the usual set of hydrodynamic variables is extended to include the presence of very slowly decaying defect densities. The long time limit of the density correlation function, the nonergodicity parameter, is studied in the vicinity of the dynamic transition point, and scaling exponents with respect to the distance from the critical point are obtained. In addition to the usual square root cusp, we also see a linear dependence on distance from transition with respect to the metastability parameters. We analyze the power law relaxation of the density correlation function at the initial stage of the dynamics, and obtain an exponent dependent on temperature. Results are compared with data obtained from light scattering experiments.