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Diomba Sambou
A criterion for the existence of nonreal eigenvalues for a Dirac operator view print
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| Published: |
June 24, 2016 |
| Keywords: |
Dirac operators, complex perturbations, discrete spectrum, nonreal eigenvalues |
| Subject: |
Primary 35P20; Secondary 81Q12, 35J10 |
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Abstract
The aim of this work is to explore the discrete spectrum
generated by complex perturbations in L2(R3,C4)
of the 3d Dirac operator
α ⋅ (-i∇ - A) + m β
with variable magnetic
field. Here, α := (α1,α2,α3) and
β are 4 × 4 Dirac matrices, and m > 0 is
the mass of a particle. We give a simple criterion for the
potentials to generate discrete spectrum near ± m. In
case of creation of nonreal eigenvalues, this criterion
gives also their location.
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| Acknowledgements
This work is partially supported by the Chilean Program Núcleo Milenio de Física Matemática RC120002.
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| Author information
Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago de Chile
disambou@mat.uc.cl
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