Absence of high-energy spectral concentration for Dirac systems with divergent potentials

Eastham, Michael S. P. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2005. Absence of high-energy spectral concentration for Dirac systems with divergent potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135 (4) , pp. 689-702. 10.1017/S0308210500004078

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Abstract

It is known that one-dimensional Dirac systems with potentials q which tend to −∞ (or ∞) at infinity, such that 1/q is of bounded variation, have a purely absolutely continuous spectrum covering the whole real line. We show that, for the system on a half-line, there are no local maxima of the spectral density (points of spectral concentration) above some value of the spectral parameter if q satisfies certain additional regularity conditions. These conditions admit thrice-differentiable potentials of power or exponential growth. The eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end-point.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics Mathematics
Additional Information:	PDF uploaded in accordance with publisher's policy as of 28/7/14.
Publisher:	Royal Society of Edinburgh
ISSN:	14737124
Date of First Compliant Deposit:	30 March 2016
Last Modified:	07 May 2023 09:15
URI:	https://orca.cardiff.ac.uk/id/eprint/1696

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