Destruction of Anderson localization by subquadratic nonlinearity

Abstract

Abstract It is shown based on a mapping procedure onto a Cayley tree that a subquadratic nonlinearity destroys Anderson localization of waves in nonlinear Schrödinger lattices with randomness, if the exponent of the nonlinearity satisfies , giving rise to unlimited subdiffusive spreading of an initially localized wave packet along the lattice. The focus on subquadratic nonlinearity is intended to amend and generalize the special case s = 1, considered previously, by offering a more comprehensive picture of dynamics. A transport model characterizing the spreading process is obtained in terms of a bifractional diffusion equation involving both long-time trappings of unstable modes on finite clusters and their long-haul jumps in wave number space consistent with Lévy flights. The origin of the flights is associated with self-intersections of the higher-order Cayley trees with odd coordination numbers z > 3 leading to degenerate states.