2023/12/14 by Chong-Son Dröge, Dröge, Chong-Son, Anna Weller +1
Chemistry · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Molecular spectroscopy and chirality #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2312.09116
openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that quantum graph eigenvalues can be found as the solutions of a nonlinear eigenvalue problem, and in the special case of equilateral graphs, even as the solutions of a linear eigenvalue problem on the underlying combinatorial graph. The latter, remarkable relation to combinatorial graph spectra will be exploited to derive a solver for the general, non-equilateral case. Eigenvalue estimates from equilateral approximations will be applied as initial guesses in a Newton-trace iteration to solve the nonlinear eigenvalue problem.