Chaos at the Crossroads of Spontaneous Symmetry Breakings: Novel Universality Classes

This thesis investigates quantum systems with underlying classically chaotic dynamics in the framework of spontaneous symmetry-breaking transitions. The main emphases are on: (i) Quantum-Classical correspondence in systems at a metal-to-insulator transition as seen through dynamical stability with respect to external perturbations, and (ii) the spontaneous breaking of combined parity and time-reversal symmetry in nonHermitian systems across the localization-delocalization transition. By studying such “crossroads” between a critical phase transition and a parametric system change (quantum to classical or localized to delocalized) we are able to develop results for entire universality classes.