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

A. A. Balinsky·W. D. Evans·Roger T. Lewis
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Abstract

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.

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A. A. Balinsky, W. D. Evans, Roger T. Lewis. 1999-11-09. Semi-classical asymptotics for the counting functions and Riesz means of Pauli and Dirac operators with large magnetic fields. https://arxiv.org/abs/math-ph/9911013

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