Spectra of Half-Infinite Quantum Graph Tubes

Abstract

Carbon nanotubes are a feverishly-studied topic in the scientific community as of late. Mathematically, they can be modeled with a quantum graph. Here we consider a structure somewhat similar to carbon nanotubes, another quantum graph that is formed by rolling a square lattice instead of a graphene structure. This symmetry imposes properties that make certain motions easier to study by creating convenient pairs of incoming and outgoing motions.