Studies of Structured Disorder in Classical Many-Body and Quantum Network Systems

Abstract

Disorder is ubiquitous in nature, but can be realized in a myriad of ways, each with differing effects on the physical properties of the system under study. In this thesis, we conduct studies of disordered hyperuniform classical systems and open quantum systems modeled after molecular exciton networks. In hyperuniform systems, the long-range density fluctuations asymptotically grow with the same order as a crystal. In Ch. 2, we investigate the Barlow packings, which are the stacking variations of the close-packing of equal spheres. These systems are hyperuniform, but can exhibit stacking disorder. We compute the hyperuniformity order metric of these packings. Despite this metric describing the density fluctuations at large length scales, we find that, for these packings, it is almost-linearly determined by the fraction of hcp-like local clusters. In Ch. 3, we study the nearest-neighbor functions of disordered stealthy hyperuniform many-particle systems in the low-temperature limit. These systems have a gap in their structure factor (or single-scattering intensity), and they undergo a disorder-to-order transition as an increasing gap fixes more degrees of freedom. They can also be shown to have a bounded hole size. Using an accurate approximation for the pair correlation function, we obtain short-range approximations and proposed bounds on the nearest-neighbor functions. We then investigate the behavior near the critical-hole size, and propose accurate expressions across all length scales. Finally, in Ch. 4, we look at the influence of the interaction topology, decoherence, and static disorder on open quantum exciton-like networks. We find that certain interaction graphs and decoherence models, such as the star graph under collective de-excitation, can force the eigenvalues to spread in a symmetric manner with increasing site energy disorder. On the other hand, the susceptibility to disorder found in topologies like the nearest-neighbor graph can help protect the first-excited state population against collective excitation loss. We also investigate disordered all-to-all interactions and topological disorder. These results expand the library of examples in which knowledge of the precise correlations and interactions responsible for disorder is needed to understand the geometric and physical properties of the system.