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Dirac operators on the half-line: stability of spectrum and non-relativistic limit

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arxiv 2405.10009 v1 pith:G2VUD3GR submitted 2024-05-16 math.SP math-phmath.APmath.MPquant-ph

David Kramar , David Krejcirik This is my paper · ORCID
classification math.SPmath-phmath.APmath.MPquant-ph
keywords half-lineconditionsdiraclimitnon-relativisticoperatorsspectrumstability
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We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations and study the optimality of the obtained results. Finally, we establish a non-relativistic limit which makes a relationship of the present model to the Robin Laplacian on the half-line.

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  1. The relativistic rotated harmonic oscillator

    math.SP 2024-11 accept novelty 6.0 of 10

    A new relativistic Dirac oscillator with a complex rotation has real discrete spectrum but wild eigenfunctions and pseudospectra; the eigenprojector growth rate equals a known rotated-oscillator quantity.

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