Absolutely continuous spectrum of Dirac operators with square-integrable potentials

Hughes, Daniel and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2014. Absolutely continuous spectrum of Dirac operators with square-integrable potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144 (3) , pp. 533-555. 10.1017/S0308210512001187

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Abstract

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞, −1] ∪ [1, ∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function. Furthermore, we show that the absolutely continuous spectrum persists when an angular momentum term is added, thus also establishing the result for spherically symmetric Dirac operators in higher dimensions.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Cambridge University Press
ISSN:	0308-2105
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	4 March 2013
Last Modified:	30 Nov 2024 21:00
URI:	https://orca.cardiff.ac.uk/id/eprint/60369

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