Simple picture of supercooled liquid dynamics: dynamic scaling and phenomenology based on clusters

Although it is now well established that in glassy liquids, slow structural relaxation accompanies a correlated structural rearrangement, the role of such a correlation in the transport anomaly, and thus in the slow dynamics, remains unclear. In this paper, we argue from a hydrodynamic viewpoint that a correlated structure (cluster) with a characteristic size ξ sustains the long-lived stress and dynamically couples with the hydrodynamic fluctuations; therefore, the dynamics of this cluster is the origin of the mesoscopic nature of anomalous hydrodynamic transport. Based on this argument, we derive a dynamic scaling law for τ(α) (or η, where η is the macroscopic shear viscosity) as a function of ξ: τ(α)([proportionality]η)[proportionality]ξ(4). We provide a simple explanation for basic features of anomalous transport, such as the breakdown of the Stokes-Einstein relation and the length-scale-dependent decoupling between viscosity and diffusion. The present study further suggests a different physical picture: Through the coarse graining of smaller-scale fluctuations (