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

Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 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:	02 May 2023 12:49
URI:	https://orca.cardiff.ac.uk/id/eprint/26492

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