Numerical analysis of nodal sets for eigenvalues of Aharonov-Bohm Hamiltonians on the square and application to minimal partitions
Résumé
Using the double covering approach introduced by B. Helffer, M. and T. Hoffmann-Ostenhof and M. Owen and further developed for questions of isospectrality by the authors in collaboration with T. Hoffmann-Ostenhof, we analyze the variation of the eigenvalues of the one pole Aharonov-Bohm Hamiltonian on the square and the nodal picture of the associated eigenfunctions as a function of the pole. This leads us to discover new candidates for minimal $k$-partitions of the square with a specific topological type. This illustrates also recent results of B. Noris and S. Terracini. This finally supports or disproves conjectures for the minimal $3$ and $5$-partitions on the square.
Origine : Fichiers produits par l'(les) auteur(s)
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