A modified local Weyl law and spectral comparison results for ${\delta }^{\prime }$-coupling conditions

Abstract

We study Schrödinger operators on compact finite metric graphs subject to ${\delta }^{\prime }$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjoint realisations on a given graph. Furthermore, using this spectral comparison result, we also study the limiting mean eigenvalue distance comparing ${\delta }^{\prime }$-coupling conditions to so-called anti-Kirchhoff conditions, showing divergence and thereby confirming a numerical observation in [arXiv:2212.12531]. .

12 pages, 1 figure; comments are welcome!

References in corpus (4)

• Comparing the spectrum of Schrödinger operators on quantum graphs
• Differences between Robin and Neumann eigenvalues on metric graphs
• A note on Ambarzumian's theorem for quantum graphs
• Some spectral comparison results on infinite quantum graphs