We study how the eigenvalues of a magnetic Schrödinger operator of Aharonov-Bohm type depend on the singularities of its magnetic potential. We consider a magnetic potential defined everywhere in the plane except at a finite number of singularities, so that the associated magnetic field is zero. On a fixed planar domain, we define the corresponding magnetic Hamiltonian with Dirichlet boundary conditions, and study its eigenvalues as functions of the singularities. We prove that these functions are continuous, and in some cases even analytic. We sketch the connection of this eigenvalue problem to the problem of finding spectral minimal partitions of the domain.

Eigenvalues variations for Aharonov-Bohm operators

LENA, CORENTIN
2015-01-01

Abstract

We study how the eigenvalues of a magnetic Schrödinger operator of Aharonov-Bohm type depend on the singularities of its magnetic potential. We consider a magnetic potential defined everywhere in the plane except at a finite number of singularities, so that the associated magnetic field is zero. On a fixed planar domain, we define the corresponding magnetic Hamiltonian with Dirichlet boundary conditions, and study its eigenvalues as functions of the singularities. We prove that these functions are continuous, and in some cases even analytic. We sketch the connection of this eigenvalue problem to the problem of finding spectral minimal partitions of the domain.
2015
56
1
11
28
http://scitation.aip.org/content/aip/journal/jmp/56/1/10.1063/1.4905647
https://hal.archives-ouvertes.fr/hal-00959975
Analysis; Eigenvalues; Mathematical Physics; Partial Differential Equations; Perturbation Theory; Spectral Theory; Aharonov-Bohm Hamiltonians; Nodal Domains; Minimal Partitions
Léna, Corentin
File in questo prodotto:
File Dimensione Formato  
ArticleAB.pdf

Accesso aperto

Descrizione: Main article
Tipo di file: PREPRINT (PRIMA BOZZA)
Dimensione 417.33 kB
Formato Adobe PDF
417.33 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1548476
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 16
social impact