Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph

Abstract

In this paper, we consider periodic Schrödinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.

Keywords

• quantum graph
• spectral gap
• band structure
• Hill operator