Spectra of magnetic chain graphs: coupling constant perturbations. (4th March 2015)

• Record Type: Journal Article
• Authors: Exner, Pavel; Manko, Stepan S
• Is Part Of: Journal of physics. Volume 48:Number 12(2015)
• Publication Date: 2015-03-04
• Subjects: quantum graph -- magnetic field -- coupling constant perturbation -- eigenvalues in gaps -- weak coupling; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/12/125302
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We analyze spectral properties of a quantum graph in the form of a ring chain with a δ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the chain exhibits a translational symmetry and study the discrete spectrum in the gaps resulting from changing a finite number of vertex coupling constants. In particular, we discuss in detail some examples such as perturbations of one or two vertices, weak perturbation asymptotics, and a pair of distant perturbations.