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Nonlinear Anderson localized states at arbitrary disorder
Published 1 Jan 2022 in math-ph, math.AP, math.DS, and math.MP | (2201.00173v1)
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 Schr\"odinger 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.
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