Glass transition in granular media

– In the framework of schematic hard spheres lattice models for granular media we investigate the phenomenon of the " jamming transition ". In particular, using Edwards' approach, by analytical calculations at a mean field level, we derive the system phase diagram and show that " jamming " corresponds to a phase transition from a " fluid " to a " glassy " phase, observed when crystallization is avoided. Interestingly, the nature of such a " glassy " phase turns out to be the same found in mean field models for glass formers. Gently shaken granular media exhibit a strong form of " jamming " [1–3], i.e., an exceedingly slow dynamics, which shows deep connections [4–6] to " freezing " phenomena observed in many thermal systems such as glass formers [7]. Although the idea of a unified description of these phenomena is emerging [5], the precise nature of jamming in non-thermal systems and the origin of its close connections to glassy phenomena in thermal ones are still open and very important issues [8]. Here, we discuss these topics in the framework of the Statistical Mechanics of powders introduced by Edwards' [9–11] where, to allow theoretical calculations, it is assumed that time averages of a system subject to some drive (e.g., " tapping ") coincide with suitable ensemble averages over its " mechanically stable " states. In particular, we consider a schematic model for granular media recently shown [11] to be well described by Edwards' assumption: a system of hard spheres under gravity confined on a cubic lattice. In this letter we first show that this model subject to a Monte Carlo (MC) " tap dynamics " , when crystallization is avoided, has a pronounced jamming similar to the one found in experiments [1–3]. We then discuss the nature of such a form of jamming by analytically solving Edwards' partition function of the system at a mean field level, by use of a Bethe approximation. This approach shows that the present model for granular media undergoes a phase transition from a (supercooled) " fluid " phase to a " glassy " phase, when its crystallization transition is avoided. The nature of such a " glassy " phase results to be the same found in mean field models for glass formers [12, 13]: a discontinuous Replica Symmetry Breaking phase preceded by a dynamical freezing point. This finding quantitatively confirms early speculations about …