The Nonlinear Anderson Problem - A Vital Challenge in Wave Localization

Explore a comprehensive seminar talk examining Anderson localization and its relationship with nonlinear dynamics in disordered media. Delve into how P. W. Anderson's fundamental concept of wave localization in disordered systems can be disrupted by nonlinear interactions, potentially allowing infinite wave propagation above critical thresholds. Learn about various theoretical models and numerical demonstrations, including discrete nonlinear Schrödinger equations with random potential, continuous time random walks, chaos theory, percolation, fractional kinetics, and Cayley trees. Examine the implications of subquadratic power nonlinearity as a form of long-range self-interaction and its effects on asymptotic wave spreading. Gain insights from Dr. Alexander Milovanov's expertise at ENEA C.R. Frascati, drawing from recent research published in Physical Review E.