Nonlinear Anderson localized states at arbitrary disorder
Mathematical Physics
2022-01-04 v1 Analysis of PDEs
Dynamical Systems
math.MP
Abstract
It is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL 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.
Cite
@article{arxiv.2201.00173,
title = {Nonlinear Anderson localized states at arbitrary disorder},
author = {Wencai Liu and W. -M. Wang},
journal= {arXiv preprint arXiv:2201.00173},
year = {2022}
}
Comments
40 pages