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arXiv · 2312.00181

On two-dimensional Dirac operators with $\delta$-shell interactions supported on unbounded curves with straight ends

Jussi Behrndt·Pavel Exner·Markus Holzmann·Matěj Tušek
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Abstract

In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a smooth unbounded curve that is straight outside a compact set and whose ends are rays that are not parallel to each other. For all possible combinations of interaction strengths we describe the self-adjoint realizations and compute their essential spectra. Moreover, we prove in different situations the existence of geometrically induced discrete eigenvalues.

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Jussi Behrndt, Pavel Exner, Markus Holzmann, Matěj Tušek. 2023-11-30. On two-dimensional Dirac operators with $\delta$-shell interactions supported on unbounded curves with straight ends. https://arxiv.org/abs/2312.00181

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