Glass elasticity from particle trajectories.

Using positional data from video microscopy of a two-dimensional colloidal system and from simulations of hard disks, we determine the wave-vector-dependent elastic dispersion relations in glass. The emergence of rigidity based on the existence of a well defined displacement field in amorphous solids is demonstrated. Continuum elastic theory is recovered in the limit of long wavelengths which provides the glass elastic shear and bulk modulus as a function of temperature. The onset of a finite static shear modulus upon cooling marks the fluid-glass transition in an intuitive and unique way.