A few inverse problems in classical statistical mechanics and photonics
Mikael Rechtsman, CIMS

Recent developments in colloidal science have allowed experimentalists to tailor the isotropic interactions between nanometer and micron-sized objects, yielding a variety of exotic many-body phases of (soft) matter.  A ``holy grail'' of the field has been the self-assembly of dielectric structures with full photonic bandgaps, which have enormous technological application (waveguiding, optical computing, etc.), a typical example being the diamond lattice of spheres.

In the first part of the talk, I will discuss the problem of deriving isotropic inter-particle pair potentials that yield targeted, technologically relevant and exotic crystal structures (including diamond); I will also show how isotropic potentials may be derived to give rise to negative thermal expansion and negative Poisson's ratio materials.  These exceptional materials properties have not previously been found in isotropic systems.

In the second part, I will go deeper into the problem of finding and optimizing dielectric patterns that have large photonic bandgaps.  Quasicrystals are aperioidic structures with long-ranged orientational order; I will explain why they have tremendous potential to produce bandgaps and how they have been optimized to yield the largest known bandgaps in certain cases.