Glass elasticity from particle trajectories

Using positional data from video-microscopy of a two-dimensional colloidal system and from sim-ulations of hard discs 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. PACS numbers: 82.70.Dd, 61.20.Ja While fluids flow with a finite viscosity, solids respond elastically to deformation. At the glass transition, a su-percooled liquid transforms into a disordered solid which possesses mechanical rigidity to shear deformations. The corresponding elastic constant is the shear modulus µ [1]. In crystalline solids, shear rigidity results from the long-ranged correlations of displacements heralding the break-ing of translational invariance. The transverse acoustica