Approximate zero modes for the Pauli operator on a region

作者：Elton Daniel M^*

来源：Journal of Spectral Theory, 2016, 6(2): 373-413.

DOI：10.4171/JST/127

• Pauli operator
• eigenvalue asymptotics
• approximate zero modes

Let P-Omega,P-t A denoted the Pauli operator on a bounded open region Omega subset of R-2 with Dirichlet boundary conditions and magnetic potential A scaled by some t > 0. Assume that the corresponding magnetic field B = curl A satisfies B is an element of L log L(Omega) boolean AND C-alpha (Omega(0)) where alpha > 0 and Omega(0) is an open subset of Omega of full measure (note that, the Orlicz space L log L (Omega) contains L-P (Omega) for any p > 1). Let N-Omega,N-t A(lambda) denote the corresponding eigenvalue counting function. We establish the strong field asymptotic formula
N-Omega,N-t A(lambda(t)) = t/2 pi integral(Omega) vertical bar B(x)vertical bar dx + o(t)
as t -> +infinity, whenever lambda(t) = Ce-ct sigma for some sigma is an element of (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 R-2.

• 出版日期2016