Destruction of Anderson localization by subquadratic nonlinearity

¹ ENEA National Laboratory, Centro Ricerche Frascati - I-00044 Frascati, Rome, Italy
² Department of Physics, Technion, Israel Institute of Technology - 32000 Haifa, Israel
³ Max Planck Institute for the Physics of Complex Systems - D-01187 Dresden, Germany

^(a) E-mail: alexander.milovanov@enea.it (corresponding author)

Received: 8 December 2022
Accepted: 6 March 2023

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.