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

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

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 Fundame...

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Veröffentlicht in:arXiv.org 2024-12
1. Verfasser: Baur, Matthias
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Eigenvalues
Magnetic fields
Magnetic flux
Optimization
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description 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.
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subjects Eigenvalues
Magnetic fields
Magnetic flux
Optimization
title Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field
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