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A theory for the nonlocal shear stress correlations in supercooled liquids and colloidal suspensions is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. Whereas Eshelby‘s elasticity pattern is recovered independently of the dynamics, the Goldstone modes differ drastically: Newtonian dynamics leads to propagating transverse sound, while the Goldstone modes of a colloidal glass are diffusive. Precursors of the long-ranged anisotropic stress correlations in the fluid can be observed in both cases. Their spatial extent can be characterized by a correlation length, which grows like the shear viscosity for a Newtonian fluid and like its square root in a colloidal fluid. These results are derived within a hydrodynamic theory, generalising Maxwell‘s model to finite wavenumbers, after the dynamics has been decomposed into potentially slow modes, associated with conservation laws and/or the order parameter, and fast microscopic degrees of freedom.

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Annette Zippelius, Georg-August-Universitat Göttingen
Online via zoom
Contact: Martin Zirnbauer