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Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials

Schmidt, Karl Michael and Umeda, Tomio 2015. Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials. Letters in Mathematical Physics 105 (11) , 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
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: The final publication is available at http://link.springer.com/article/10.1007%2Fs11005-015-0799-1.
Publisher: Springer Verlag
ISSN: 0377-9017
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 10 August 2015
Last Modified: 27 Jun 2019 17:37
URI: http://orca.cf.ac.uk/id/eprint/75636

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