Spectrum of the Iwatsuka Hamiltonian at thresholds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:460

Article

Miranda, Pablo¹  Popoff, Nicolas² 

[1] Univ Santiago Chile, Dept Matemat & Ciencia Comp, Las Sophoras 173, Santiago, Chile

[2] Univ Bordeaux, IMB, UMR 5251, F-33405 Talence, France

关键词: Magnetic Laplacian;    Asymptotics of band functions;    Current estimates;    Spectral Shift Function;   

DOI  :  10.1016/j.jmaa.2017.11.058

来源: Elsevier

【 摘 要 】

We consider the bi-dimensional Schrodinger operator with unidirectionally constant magnetic field, Ho, sometimes known as the Iwatsuka Hamiltonian. This operator is analytically fibered, with band functions converging to finite limits at infinity. We first obtain the asymptotic behavior of the band functions and its derivatives. Using this results we give estimates on the current and on the localization of states whose energy value is close to a given threshold in the spectrum of Ho. In addition, for non-negative electric perturbations V we study the spectral properties of H-0 +/- V, by considering the Spectral Shift Function associated to the operator pair (H-0 +/- V, H-0). We compute the asymptotic behavior of the Spectral Shift Function at the thresholds, which are the only points where it can grow to infinity. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free