Generation and Structural Characterization of Stealthy Hyperuniform Many-Particle Systems*

Hyperuniform many-particle systems are characterized by an anomalous suppression of large-scale density fluctuations compared to typical disordered systems (e.g., liquids) [1]. This classification includes crystals, quasicrystals and exotic amorphous systems. Disordered hyperuniform systems are now known to arise in a variety of contexts in physics, mathematics and biology. Stealthy hyperuniform systems represent the strongest form of hyperuniformity as they suppress single scattering events from infinite wavelengths down to intermediate wavelengths and are endowed with novel physical properties [2]. It has been shown that stealthy hyperuniform systems can be generated as the ground states of soft bounded pair interactions using the so-called collective-coordinate optimization scheme; see Ref. 2 and references therein. While considerable progress has been made in the generation and structural characterization of such systems, there are many open questions concerning the precise nature of the ground-state manifold and the phase transition from disordered to ordered states as a function of the stealthiness parameter. We shed light on these issues using the collective-coordinate approach for stealthy hyperuniform systems across Euclidean space dimensions.

1. S. Torquato and F. H. Stillinger, Local Density Fluctuations, Hyperuniform Systems, and Order Metrics, Physical Review E, 68, 041113 1-25 (2003).

2. S. Torquato, Hyperuniform States of Matter, Physics Reports, 745, 1-95 (2018).