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Spectral band structure of periodic Schrödinger operators on a generalized degenerate zigzag nanotube. (English) Zbl 1337.34087

Summary: We refer generalized degenerate zigzag nanotubes as periodic metric graphs which consist of segments of length 1 and rings of length 2 throughout this paper. In this paper, we consider the case where there are one segment and three rings in the basic period cell and analyze the spectrum of periodic Schrödinger operators on the generalized degenerate zigzag nanotube. We obtain the relationship between the structure of the metric graph and the nondegenerate spectral gaps of the Schrödinger operators.

MSC:

34L05 General spectral theory of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34B45 Boundary value problems on graphs and networks for ordinary differential equations
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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