Hyperuniformity and beyond in complex systems

Abstract

Disordered systems and their emergent dynamics are key aspects in understanding non-equilibrium phenomena. However, the inadequacy of mean field approaches below the upper critical dimension, and the general lack of lattice symmetries or conventional measures of long range order, severely limit the available tools at hand to characterize them. In this dissertation, we introduce new theoretical perspectives and statistical tools that capture the subtle presence of hierarchical hidden order in otherwise disordered systems.