2023/04/26 by M. Fialová, Fialová, Marie
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2304.13373
openalex publication_date 2023/04/26 · openalex created_date 2023/04/28 · openalex updated_date 2026/08/02
The Aharonov-Casher theorem is a result on the number of the so-called zero modes of a system described by the magnetic Pauli operator in ℝ2. In this paper we address the same question for the Dirac operator on a flat two-dimensional manifold with boundary and Atiyah-Patodi-Singer boundary condition. More concretely we are interested in the plane and a disc with a finite number of circular holes cut out. We consider a smooth compactly supported magnetic field on the manifold and an arbitrary magnetic field inside the holes.