Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field
Optimization and Control
2025-07-18 v2 Mathematical Physics
Analysis of PDEs
math.MP
Spectral Theory
Abstract
We present numerical minimizers for the first seven eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field in a wide range of field strengths. Adapting an approach by Antunes and Freitas, we use gradient descent for the minimization procedure together with the Method of Fundamental solutions for eigenvalue computation. Remarkably, we observe that when the magnetic flux exceeds the index of the target eigenvalue, the minimizer is always a disk.
Keywords
Cite
@article{arxiv.2412.06533,
title = {Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field},
author = {Matthias Baur},
journal= {arXiv preprint arXiv:2412.06533},
year = {2025}
}
Comments
29 pages, 13 figures, 2 tables; updated to the published version