10/25 - Faculty Colloquium (theoretical): Sal Torquato
Salvatore Torquato - Complex Materials Theory Group website
Department of Chemistry
Unusual Low-Temperature States of Matter: Challenging Orthodoxy
We use inverse statistical-mechanical techniques to challenge conventional wisdom about the nature of classical low-temperature states of matter. We pose a number of unusual questions that have surprising answers. Can graphene or diamond crystal structures be the ground states of many-particle interactions that involve only non-directional (isotropic) pair potentials? Are there single-component many-particle systems characterized by isotropic pair potentials that possess exotic low-temperature bulk properties, such as negative thermal expansion or negative Poisson's ratio? Can ground states ever be disordered? In other words, can cooling a liquid to absolute zero result in a completely disordered many-particle configuration (as opposed to the usual crystal ground state)? I will show that the answers to all of these questions are in the affirmative, and have fundamental and practical implications. I then will discuss the problem of determining the densest packings of spheres in high dimensions, which is directly related to the optimal way of sending digital signals over noisy channels. We provide strong theoretical evidence for the remarkable possibility that disordered (rather than ordered) sphere packings are the densest for sufficiently large dimensions, implying the existence of disordered ground states for some continuous potentials. This is done by providing the putative exponential improvement on Minkowski's 100-year-old lower bound on the maximal packing density of spheres in high dimensions. Finally, I will describe a new view of how structural glasses are formed upon supercooling liquids.