Princeton University Department of Physics Donald R. Hamilton Colloquium Series

Abstract: The study of hyperuniform states of matter is an emerging multidisciplinary field, influencing and linking developments across the physical sciences, mathematics and biology. The hyperuniformity concept generalizes the traditional notion of long-range order to include not only all crystals and quasicrystals, but exotic disordered states of matter as well, thus providing a unified framework to quantitatively categorize such phases of matter. Disordered hyperuniform states have attracted great attention across many fields over the last two decades because they have the character of crystals in the way they suppress density fluctuations on large length scales but are isotropic like liquids.

I will review the hyperuniformity concept, its capacity to rank order correlated systems, and how it arises in sphere packings, random matrices, nontrivial zeros of the Riemann zeta function, spatial distribution of the prime numbers, free fermions, Laughlin’s incompressible quantum states, and photoreceptor mosaics in avian retina. I will also describe novel electromagnetic, transport and elastic characteristics of disordered hyperuniform materials.