Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field

Autor:	Baur, Matthias
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Mathematical Physics Mathematics - Analysis of PDEs Mathematics - Spectral Theory 35Q40 49Q10 35P15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages, 13 figures, 1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.06533 Zobrazit plný text záznamu View this record from Arxiv