Harvard Condensed Matter Theory Seminars

Matthew Wyart, Harvard University

Soft Motions and Rigidity of Amorphous Solids
We poorly understand the microscopic properties of amorphous solids, such as transport, force propagation or the nature of their mechanical rigidity. These questions seem to be related to the presence of an excess of low-frequency vibrational modes, the so-called `` Boson Peak". We explain the nature of these modes in repulsive, short-range systems. This enables to derive a microscopic criterion of rigidity, which extends a previous result of Maxwell valid in systems without pre-stress (e.g. a network of unstretched springs). This implies that rigidity is not a local property, but is characterized by a length which depends on the packing geometry, and which can be large. We argue that this description applies to granular media, silica and colloidal glasses. We infer a non-trivial property of the radial distribution function at the random close packing.

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