Collisions, caging, thermodynamics, and jamming in the barrier hopping theory of glassy hard sphere fluids

An ultralocal limit of the microscopic single particle barrier hopping theory of glassy dynamics is proposed which allows explicit analytic expressions for the characteristic length scales, energy scales, and nonequilibrium free energy to be derived. All properties are shown to be controlled by a single coupling constant determined by the fluid density and contact value of the radial distribution function. This parameter quantifies an effective mean square force exerted on a tagged particle due to collisions with its surroundings. The analysis suggests a conceptual basis for previous surprising findings of multiple inter-relationships between characteristics of the transient localized state, the early stages of cage escape, non-Gaussian or dynamic heterogeneity effects, and the barrier hopping process that defines the alpha relaxation event. The underlying physical picture is also relevant to fluids of nonspherical molecules and sticky colloidal suspensions. The possibility of a unified view of liquid dynamics is suggested spanning the range from dense gases to the zero mobility jammed state.