Signatures of Phase Transition in Wave Dynamics of Complex Systems

This thesis investigates wave dynamics and stability (against small perturbations or interactions) of complex systems where phase transition from localized to delocalized behavior can be achieved by changing an external or internal parameter. The main emphasis is on: (a) the stability of dynamics (under perturbed time-reversal experiments) of systems at a metal-to-insulator transition (MIT), (b) the effects of interaction-induced nonlinearity on wavepacket dynamics of systems at a MIT and (c) the statistical properties of current relaxation of systems where a nonlinearity-induced localization-delocalization phase transition occurs.