Spectra of Half-Infinite Quantum Graph Tubes

TL;DR

This paper studies the spectral properties of a quantum graph model resembling carbon nanotubes, specifically a square lattice tube, to facilitate analysis of wave motions in such structures.

Contribution

It introduces a new quantum graph model based on a square lattice tube, differing from traditional graphene-based nanotubes, and explores its spectral characteristics.

Findings

Simplified analysis of wave motions due to symmetry

Identification of spectral properties specific to square lattice tubes

Potential applications in nanostructure modeling

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.