Rigidity in Condensed Matter and Its Origin in Configurational Constraint.

Motivated by the formal argument that a nonzero shear modulus is the result of averaging over a constrained configuration space, we demonstrate that the shear modulus calculated over a range of temperatures and averaging times can be expressed (relative to its infinite frequency value) as a single function of the mean squared displacement. This result is shown to hold for both a glass-liquid and a crystal-liquid system.