Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

Cuenin, Jean-Claude; Laptev, Ari; Tretter, Christiane (2014). Eigenvalue estimates for non-selfadjoint Dirac operators on the real line. Annales Henri Poincaré, 15(4), pp. 707-736. Springer 10.1007/s00023-013-0259-3

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We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Cuenin, Jean-Claude and Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

1424-0637

Publisher:

Springer

Language:

English

Submitter:

Mario Amrein

Date Deposited:

14 Apr 2015 15:36

Last Modified:

07 Oct 2015 10:25

Publisher DOI:

10.1007/s00023-013-0259-3

BORIS DOI:

10.7892/boris.66708

URI:

https://boris.unibe.ch/id/eprint/66708

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