Let PΩ,tA denoted the Pauli operator on a bounded open
region Ω⊂R2 with Dirichlet boundary conditions and
magnetic potential A scaled by some t>0. Assume that the corresponding
magnetic field B=curlA satisfies B∈LlogL(Ω)∩Cα(Ω0) where α>0 and Ω0 is an open subset of
Ω of full measure (note that, the Orlicz space LlogL(Ω)
contains Lp(Ω) for any p>1). Let NΩ,tA(λ)
denote the corresponding eigenvalue counting function. We establish the strong
field asymptotic formula NΩ,tA(λ(t))=2πt∫Ω∣B(x)∣dx+o(t) as t→+∞, whenever
λ(t)=Ce−ctσ for some σ∈(0,1) and c,C>0. The
corresponding eigenfunctions can be viewed as a localised version of the
Aharonov-Casher zero modes for the Pauli operator on R2.Comment: 28 pages; for the sake of clarity the main results have been
reformulated and some minor presentational changes have been mad