Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Umeda, Tomio 2015. Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials. Letters in Mathematical Physics 105 , pp. 1479-1497. 10.1007/s11005-015-0799-1 |
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Abstract
The spectra of massless Dirac operators are of essential interest, e.g., for the electronic properties of graphene, but fundamental questions such as the existence of spectral gaps remain open. We show that the eigenvalues of massless Dirac operators with suitable real-valued potentials lie inside small sets easily characterized in terms of properties of the potentials, and we prove a Schnol-type theorem relating spectral points to polynomial boundedness of solutions of the Dirac equation. Moreover, we show that, under minimal hypotheses which leave the potential essentially unrestrained in large parts of space, the spectrum of the massless Dirac operator covers the whole real line; in particular, this will be the case if the potential is nearly constant in a sequence of regions.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Publisher: | Springer Verlag |
ISSN: | 0377-9017 |
Date of First Compliant Deposit: | 30 March 2016 |
Date of Acceptance: | 10 August 2015 |
Last Modified: | 18 Nov 2024 08:00 |
URI: | https://orca.cardiff.ac.uk/id/eprint/75636 |
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