Gaps in the spectrum of a periodic quantum graph with periodically distributed -type interactions. (2nd June 2015)

• Record Type: Journal Article
• Authors: Barseghyan, Diana; Khrabustovskyi, Andrii
• Is Part Of: Journal of physics. Volume 48:Number 25(2015)
• Publication Date: 2015-06-02
• Subjects: periodic quantum graphs -- δ′-type interactions -- spectral gaps; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/25/255201
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider a family of quantum graphs, where Γ is a -periodic metric graph and the periodic Hamiltonian is defined by the operation on the edges of Γ and either -type conditions or the Kirchhoff conditions at its vertices. Here is a small parameter. We show that the spectrum of has at least m gaps as ( is a predefined number), moreover the location of these gaps can be nicely controlled via a suitable choice of the geometry of Γ and of coupling constants involved in -type conditions.