Eigenvalue Estimates for Non-Selfadjoint Dirac Operators on the Real Line
File(s)
Accepted version
Author(s)
Cuenin, J-C
Laptev, A
Tretter, C
Type
Journal Article
Abstract
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 Schr¨odinger 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.
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 Schr¨odinger 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.
Date Issued
2013-06-03
Date Acceptance
2013-06-01
Citation
Annales Henri Poincaré, 2013, 15, pp.707-736
ISSN
1424-0637
Publisher
Springer
Start Page
707
End Page
736
Journal / Book Title
Annales Henri Poincaré
Volume
15
Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-013-0259-3
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Particles & Fields
Physics, Mathematical
Physics
PHYSICS, MATHEMATICAL
PHYSICS, MULTIDISCIPLINARY
PHYSICS, PARTICLES & FIELDS
SCHRODINGER-OPERATORS
COMPLEX POTENTIALS
RESONANCES
BOUNDS
Mathematical Physics
0105 Mathematical Physics
0202 Atomic, Molecular, Nuclear, Particle And Plasma Physics
Publication Status
Published