Stability of Spectral Types of Quasi-Periodic Schr\'odinger Operators With Respect to Perturbations by Decaying Potentials

Autor:	Damanik, David, Li, Xianzhe, You, Jiangong, Zhou, Qi
Rok vydání:	2022
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We consider perturbations of quasi-periodic Schr\"odinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the (almost) reducibility regime we prove that for perturbations with finite first moment, the essential spectrum remains purely absolutely continuous and the newly created discrete spectrum must be finite in each gap of the unperturbed spectrum. We also prove that for fixed phase, Anderson localization occurring for almost all frequencies in the regime of positive Lyapunov exponents is preserved under exponentially decaying perturbations. Comment: 37 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.03113 Zobrazit plný text záznamu View this record from Arxiv