Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on\n the disk

2017/12/22 by Laura Abatangelo, Abatangelo, Laura
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.1712.08380

Abstract

It is known that the first eigenvalue for Aharonov--Bohm operators with\nhalf-integer circulation in the unit disk is double if the potential's pole is\nlocated at the origin. We prove that in fact it is simple as the pole a\≠\n0.\n

Related

• On multiple eigenvalues for Aharonov-Bohm operators in planar domains
• Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole
• On Aharonov-Bohm operators with multiple colliding poles of any circulation
• Quantitative spectral stability for Aharonov-Bohm operators with many coalescing poles
• Sharp asymptotic estimates for eigenvalues of Aharonov-Bohm operators with varying poles