Nonlinear fluctuating hydrodynamics and sequence of time scales of relaxation in supercooled liquids

Abstract

Nonlinear fluctuating hydrodynamic (NFH) models for relaxation in the supercooled liquid are considered. Recent results on self consistent mode coupling theory for the slow relaxation of density fluctuations are analyzed to explain the glassy dynamics. The relaxation mechanisms for different types of models with and without wave vector dependences are discussed. For the schematic models where all wave vector dependences are dropped a sequence of time scales enters the relaxation process. For the non-ergodicity parameter very close to the ideal transition point is scaled by an exponent equal to 1/2. This is demonstrated here through an analysis of the mode-coupling equations for the wave vector dependent models that follow from equations of NFH.