Document Type

Article

Publication Date

10-1-2016

Abstract

The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half of the tube. The eigenfunctions associated to the spectrum of the half-tube involve all Floquet modes of the full tube. This requires solving the complex dispersion relation D(λ, k1, k2) = 0 with (k1, k2) ∈ (C/ 2 πZ) 2 subject to the constraint ak1+ bk2≡ 0 (mod 2 π), where a and b are integers. The number of Floquet modes for a given λ∈ R is 2 max {a, b}. Rightward and leftward modes are determined according to an indefinite energy flux form. The spectrum may contain eigenvalues that depend on the boundary conditions, and some eigenvalues may be embedded in the continuous spectrum.

Publication Source (Journal or Book title)

Letters in Mathematical Physics

First Page

1317

Last Page

1343

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