Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori. (March 2022)

• Record Type: Journal Article
• Authors: Bambusi, Dario; Langella, Beatrice; Montalto, Riccardo
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: 37K10 -- 35Q55; Schrödinger operator -- Spectral asymptotics -- Normal form -- Pseudo differential operators -- Nekhoroshev theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112679
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study Schrödinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in λ − δ with δ ∈ ( 0, 1 ) for most of the eigenvalues λ (stable eigenvalues), while it is a "directional expansion" for the remaining eigenvalues (unstable eigenvalues). The proof is based on a structure theorem which is a variant of the one proved in [31, 32] and on a new iterative quasimode argument.