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.
Mathematics Subject Classification: 34L05, 34L15, 34B45.