Spectral transition for Dirac operators with electrostatic $\delta$-shell potentials supported on the straight line

Jussi Behrndt; Markus Holzmann; Matěj Tušek

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arXiv · 2107.01156

Spectral transition for Dirac operators with electrostatic $\delta$-shell potentials supported on the straight line

Jussi Behrndt·Markus Holzmann·Matěj Tušek

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Abstract

In this note the two dimensional Dirac operator $A_\eta$ with an electrostatic $\delta$-shell interaction of strength $\eta\in\mathbb R$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths $\eta=\pm 2$ the continuous spectrum of $A_\eta$ inside the spectral gap of the free Dirac operator $A_0$ collapses abruptly to a single point.

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BibTeX RIS

Jussi Behrndt, Markus Holzmann, Matěj Tušek. 2021-07-02. Spectral transition for Dirac operators with electrostatic $\delta$-shell potentials supported on the straight line. https://arxiv.org/abs/2107.01156

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