Dynamical Systems Seminar

Although discussed since ancient times, the origin of rigidity in materials remains a disputed topic. How can a material be rigid when its atoms must be in perpetual motion? The finite temperature liquid-to-solid transition is discontinuous, owing to the accompanying breaking of the translational symmetry. The periodicity and anisotropy of the solid, if any, render the transition sharp but are not essential. Rigid aperiodic solids range from piles of sand, for which thermal effects are indeed negligible, to glasses, which are rigid despite vigorous thermal motion at the microscopic level. The former are mechanically jammed, while the latter are made by thermally quenching an equilibrated liquid. The thermal, rheological, and electronic behaviors of glasses exhibit many universal features. I will explain how these can be understood quantitatively. The latter quantitative description excludes jamming as the mechanism of the structural glass transition and crystal formation alike. In fact, jammed and finite-temperature aperiodic solids can be thought of states as two distinct phases on a generalized phase diagram containing off-equilibrium states.