Work

Explicit construction of Gevrey Quasi-Periodic Discrete Schrödinger operators with cantor spectrum

Year: 2025

Type: article

Abstract: We construct 1-dim difference Schrödinger operators with a class of Gevrey potentials such that the Cantor spectrum occurs together with the estimations of open spectral gaps for $ 0<|\lambda|\leq 1 $. The proof is based on KAM1 and the Moser-Pöschel argument.1KAM is the abbreviation of the Kolmogorov-Arnold-Moser Theorem.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2025156

Authors: Xuanji Hou, Li Zhang

Institution: Central China Normal University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Central China Normal University

Awards: 一维动力系统的随机稳定性, G6257605804, G6711111910