Optimization of quantum graph eigenvalues with preferred orientation vertex conditions
Mathematical Physics
2025-03-14 v2 math.MP
Spectral Theory
Abstract
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which the ground state eigenvalue is maximized. Furthermore, for general finite metric graphs we provide upper bounds for all eigenvalues.
Cite
@article{arxiv.2410.21820,
title = {Optimization of quantum graph eigenvalues with preferred orientation vertex conditions},
author = {Pavel Exner and Jonathan Rohleder},
journal= {arXiv preprint arXiv:2410.21820},
year = {2025}
}