Work

Nonlinear Anderson localized states at arbitrary disorder

Year: 2022

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2201.00173

Authors: Liu, Wencai, Wang, W. -M.

Institutions: Centre National de la Recherche Scientifique, CY Cergy Paris Université, Université de Cergy-Pontoise, Texas A&M University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Agence Nationale de la Recherche

Awards: G1146847238, G1185957321, Hamiltonian Systems and Related Phenomena, G5420063140, PSI, FRG: Collaborative Research: Non-Perturbative Analysis for Multi-Dimensional Quasiperiodic Systems

OpenAlex ID: W4225583330

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Cited by: 2

Related to: 10