On resonant spectral gap opening in quantum graph networks

TL;DR

This paper explores how inserting internal structures into the vertices of a regular quantum graph can create and manipulate spectral gaps, advancing understanding of spectral properties in quantum graph networks.

Contribution

It introduces methods for inducing and controlling spectral gaps in quantum graphs through vertex modifications, a novel approach in quantum graph theory.

Findings

Spectral gaps can be created by vertex modifications.

Manipulation of spectral gaps is possible through internal structures.

Results provide new tools for quantum graph spectral engineering.

Abstract

In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned for another publication.