2134/10260686.v1
Jean-Claude Cuenin
Ari Laptev
Christiane Tretter
Eigenvalue estimates for non-selfadjoint dirac operators on the real line
2019
Loughborough University
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Particles & Fields
Physics, Mathematical
Physics
SCHRODINGER-OPERATORS
COMPLEX POTENTIALS
RESONANCES
BOUNDS
Mathematical Physics
Atomic, Molecular, Nuclear, Particle and Plasma Physics
2019-11-07 09:46:42
article
https://repository.lboro.ac.uk/articles/journal_contribution/Eigenvalue_estimates_for_non-selfadjoint_dirac_operators_on_the_real_line/10260686
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.