Fluctuating phases and fluctuating relaxation times in glass forming liquids

We provide a theoretical perspective on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations to study and understand the dynamics of systems close to the glass transition at the molecular level is spelled out. We review the recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics. We then present the main theoretical approaches describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures, and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, we give an extensive overview of the most recent advances, but we also describe in some detail the important open problems that, we believe, will occupy a central place in this field in the coming years.

We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the \(N \rightarrow \infty\) limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynamic limit the system exhibits `weak' (as well as `true') ergodicity breaking and aging effects. We determine a functional Parisi-like order parameter \(P_d(q)\) which plays a similar role for the dynamics to that played by the usual function for the statics.