Nonlinear Anderson localized states at arbitrary disorder

Abstract

It is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL$(2,\mathbb{R})$ matrices, that the one dimensional random Schrödinger operator has Anderson localization at arbitrary disorder. This paper proves a nonlinear analogue, thereby establishing a KAM-type persistence result for a non-integrable system.

40 pages