Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains

Abstract

We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is established.

16 pages

References in corpus (3)

• Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
• Pauli operator and Aharonov Casher theorem for measure valued magnetic fields
• Magnetic edge states

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