Mean-field theory of hard sphere glasses and jamming

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the fcc lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g., a crystal) in low enough dimension. Still, amorphous packings have attracted much interest because for polydisperse colloids and granular materials the crystalline state is…

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  Aspen Center for Physics