Spectral properties of magnetic chain graphs

Abstract

We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start with the situation when the system has a translational symmetry and analyze spectral consequences of perturbations of various kind, such as a local change of the magnetic field, of the coupling constant, or of a ring circumference. A particular attention is paid to weak perturbations, both local and periodic; for the latter we prove a version of Saxon-Hutner conjecture.

23 pages, 2 figures. arXiv admin note: text overlap with arXiv:1412.6089

References in corpus (3)

• Quantum wires with magnetic fluxes
• Spectra of magnetic chain graphs: coupling constant perturbations
• Asymmetric quantum transport in a double-stranded Kronig-Penney model

Cited by in corpus (3)

• Zero Measure and Singular Continuous Spectra for Quantum Graphs
• Magnetic ring chains with vertex coupling of a preferred orientation
• Magnetic square lattice with vertex coupling of a preferred orientation