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Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit

Schmidt, Karl Michael 2003. Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit. Proceedings Of The American Mathematical Society 131 (4) , pp. 1205-1214.

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Abstract

A perturbation decaying to 0 at 1 and not too irregular at 0 introduces at most a discrete set of eigenvalues into the spectral gaps of a one-dimensional Dirac operator on the half-line. We show that the number of these eigenvalues in a compact subset of a gap in the essential spectrum is given by a quasi-semiclassical asymptotic formula in the slow-decay limit, which for power-decaying perturbations is equivalent to the large-coupling limit. This asymptotic behaviour elucidates the origin of the dense point spectrum observed in spherically symmetric, radially periodic three-dimensional Dirac operators.

Item Type: Article
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: First published in Proceedings Of the American Mathematical Society in Vol. 131, no.4, 2003, published by the American Mathematical Society.
Publisher: American Mathematical Society
Date of First Compliant Deposit: 30 March 2016
Last Modified: 05 Jun 2017 03:11
URI: http://orca.cf.ac.uk/id/eprint/26492

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