Semi-classical asymptotics for the counting functions and Riesz means of Pauli and Dirac operators with large magnetic fields

Balinsky, A. A.; Evans, W. D.; Lewis, Roger T.

Semi-classical asymptotics for the counting functions and Riesz means of Pauli and Dirac operators with large magnetic fields

Authors

Balinsky, A. A.

Evans, W. D.

Lewis, Roger T.

Description

We study the asymptotic behavior, as Planck's constant $\hbar\to 0$, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field $μ\mathbf{B}(x)$ and an electric field. The magnetic field strength $μ$ is allowed to tend to infinity as $\hbar\to 0$. Two main types of results are established: in the first $μ\hbar\le constant$ as $\hbar\to 0$, with magnetic fields of arbitrary direction; the second results are uniform with respect to $μ\ge 0$ but the magnetic fields have constant direction. The results on the Pauli operator complement recent work of Sobolev.