2016/01/23 by Gregory Berkolaiko, Wen Liu, Berkolaiko, Gregory +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1601.06225
openalex publication_date 2016/01/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove that after an arbitrarily small adjustment of edge lengths, the spectrum of a compact quantum graph with δ-type vertex conditions can be simple. We also show that the eigenfunctions, with the exception of those living entirely on a looping edge, can be made to be non-vanishing on all vertices of the graph. As an application of the above result, we establish that the secular manifold (also called "determinant manifold") of a large family of graphs has exactly two smooth connected components.