complexeigenvalues_revised2.pdf (318.26 kB)
0/0

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

Download (318.26 kB)
journal contribution
posted on 07.11.2019 by Jean-Claude Cuenin, Ari Laptev, Christiane Tretter
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 L 1-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. © 2013 Springer Basel.

Funding

Schweizerischer Nationalfonds, SNF, through the postdoc stipend PBBEP2 13659

SNF, grant no. 200021-119826/

DFG, grant no. TR368/6-2

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Annales Henri Poincaré

Volume

15

Issue

4

Pages

707 - 736

Publisher

Springer (part of Springer Nature)

Version

AM (Accepted Manuscript)

Rights holder

© Springer Basel

Publisher statement

This is a post-peer-review, pre-copyedit version of an article published in Annales Henri Poincaré. The final authenticated version is available online at: https://doi.org/10.1007/s00023-013-0259-3

Acceptance date

10/04/2013

Publication date

2013-06-03

Copyright date

2014

ISSN

1424-0637

eISSN

1424-0661

Language

en

Depositor

Dr Jean-Claude Cuenin Deposit date: 6 November 2019

Exports