Let denoted the the Pauli operator on a bounded open region with Dirichlet boundary conditions and magnetic potential A scaled by some . Assume that the corresponding magnetic field satisfies where and is an open subset of of full measure (note that, the Orlicz space contains for any ). Let denote the corresponding eigenvalue counting function. We establish the strong field asymptotic formula
as , whenever for some and . The corresponding eigenfunctions can be viewed as a localised version of the Aharonov–Casher zero modes for the Pauli operator on .
Cite this article
Daniel M. Elton, Approximate zero modes for the Pauli operator on a region. J. Spectr. Theory 6 (2016), no. 2, pp. 373–413DOI 10.4171/JST/127