QGLAB: A MATLAB Package for Computations on Quantum Graphs
Abstract
We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use features. The package allows one to construct a quantum graph and accurately compute the spectrum of elliptic operators, solutions to Poisson problems, the linear and nonlinear time evolution of a variety of PDEs, the continuation of branches of steady states (including locating and switching branches at bifurcations) and more. It overcomes the major challenge of discretizing quantum graphs -- the enforcement of vertex conditions -- using non-square differentiation matrices. It uses a unified framework to implement finite-difference and Chebyshev discretizations of differential operators on a quantum graph. For simplicity, the package overloads many built-in MATLAB functions to work on the class.
Cite
@article{arxiv.2401.00561,
title = {QGLAB: A MATLAB Package for Computations on Quantum Graphs},
author = {Roy H. Goodman and Grace Conte and Jeremy L. Marzuola},
journal= {arXiv preprint arXiv:2401.00561},
year = {2024}
}
Comments
41 pages, 18 figures. Major rewrite. Examples moved from appendix to body. Comments Welcome! Code associated with this publication available at https://github.com/manroygood/Quantum-Graphs/tree/master