Semi-classical Asymptotics for the Counting Functions and Riesz Means of Pauli and Dirac Operators with Large Magnetic Fields

نویسنده

  • A. A. BALINSKY
چکیده

We study the asymptotic behavior, as Planck’s constant ~ → 0, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field μB(x) and an electric field. The magnetic field strength μ is allowed to tend to infinity as ~ → 0. Two main types of results are established: in the first μ~ ≤ constant as ~ → 0, with magnetic fields of arbitrary direction; the second results are uniform with respect to μ ≥ 0 but the magnetic fields have constant direction. The results on the Pauli operator complement recent work of Sobolev.

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تاریخ انتشار 1999