Hyperuniform States of Matter and Their Extraordinary Physical Properties

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 [1]. Disordered hyperuniform states have attracted great attention across many fields over the last two decades because they have the character of crystals on large length scales but are isotropic like liquids [2]. I will review the hyperuniformity concept, its capacity to rank order correlated systems, and how it arises in sphere packings, eigenvalues of random matrices, number theory, quantum systems, and photoreceptor mosaics in avian retina. I will also describe novel electromagnetic, transport and elastic characteristics of disordered hyperuniform materials. 

1. S. Torquato and F. H. Stillinger, “Local Density Fluctuations, Hyperuniform Systems, and Order Metrics,” Phys. Rev. E, 68, 041113 (2003). 

2. S. Torquato, “Hyperuniform States of Matter,” Phys. Reports, 745, 1 (2018).

Bio: Salvatore Torquato was born in the small village of Falerna, Italy in 1954. He received his B.S. degree from Syracuse University in 1975, worked at Grumman Aerospace from 1975-1978 and received his Ph.D. degree from Stony Brook University in 1981. After a decade of being on the faculty at North Carolina State University, he joined the faculty at Princeton University. He is the Lewis Bernard Professor of Natural Sciences and Professor in the Department of Chemistry and the Princeton Materials Institute. He is also affiliated with three other departments: Physics, Applied and Computational Mathematics, and Mechanical and Aerospace Engineering. He has been a Senior Faculty Fellow in the Princeton Center for Theoretical Science. He was a Member at the Institute for Advanced Study (IAS) in Princeton on four previous occasions in the School of Natural Sciences and School of Mathematics. 

Torquato’s research work is centered in statistical physics and soft condensed matter theory. A common theme of his research is the search for unifying and rigorous principles to elucidate a broad range of phenomena, especially as it concerns the interplay between physics and geometry. Torquato has made fundamental contributions to our understanding of the nature of disorder/order in condensed phases of matter, disordered and ordered jammed states of matter, structural glasses, sphere packings in high dimensions, structure and bulk properties of disordered heterogeneous media, percolation theory, inverse statistical mechanics, self-assembly theory, degenerate ground states of many-particle and spin systems, and hyperuniform states of matter. 

Torquato has published over 475 refereed journal articles and a treatise entitled ”Random Heterogeneous Materials: Microstructure and Macroscopic Properties.” His published work has been cited about 55,000 times with an h-index of 121. He has presented over 320 invited colloquia, seminars and lectures at international conferences, national laboratories, universities, and industrial laboratories. Among other awards and honors, he is a Fellow of the American Physical Society (2004) and Society for Industrial and Applied Mathematics (2009). He received a Simons Foundation Fellowship in Theoretical Physics (2012). He was the recipient of the ACS Joel Hildebrand Award in Theoretical Chemistry of Liquids (2017), APS David Adler Lectureship Award in Material Physics (2009) and SIAM Ralph E. Kleinman Prize (2007). He was also a Guggenheim Fellow (1998).

All seminars are held on Wednesdays from 12:30 -1:30 p.m. in the Bowen Hall Auditorium Room 222. A light lunch is provided at 12:00 p.m. in the Bowen Hall Atrium immediately prior to the seminar.