English

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(2,R)(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.

Keywords

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

R2 v1 2026-06-24T08:37:30.681Z