Approximation of Dirac operators with $\boldsymbolδ$-shell potentials in the norm resolvent sense, II. Quantitative results
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916821463990272 |
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| author | Behrndt, Jussi Holzmann, Markus Stelzer-Landauer, Christian |
| author_facet | Behrndt, Jussi Holzmann, Markus Stelzer-Landauer, Christian |
| contents | This paper is devoted to the approximation of two and three-dimensional Dirac operators $H_{\widetilde{V} δ_Σ}$ with combinations of electrostatic and Lorentz scalar $δ$-shell interactions in the norm resolvent sense. Relying on results from \cite{BHS23} an explicit smallness condition on the coupling parameters is derived so that $H_{\widetilde{V} δ_Σ}$ is the limit of Dirac operators with scaled electrostatic and Lorentz scalar potentials. Via counterexamples it is shown that this condition is sharp. The approximation of $H_{\widetilde{V} δ_Σ}$ for larger coupling constants is achieved by adding an additional scaled magnetic term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of Dirac operators with $\boldsymbolδ$-shell potentials in the norm resolvent sense, II. Quantitative results Behrndt, Jussi Holzmann, Markus Stelzer-Landauer, Christian Spectral Theory This paper is devoted to the approximation of two and three-dimensional Dirac operators $H_{\widetilde{V} δ_Σ}$ with combinations of electrostatic and Lorentz scalar $δ$-shell interactions in the norm resolvent sense. Relying on results from \cite{BHS23} an explicit smallness condition on the coupling parameters is derived so that $H_{\widetilde{V} δ_Σ}$ is the limit of Dirac operators with scaled electrostatic and Lorentz scalar potentials. Via counterexamples it is shown that this condition is sharp. The approximation of $H_{\widetilde{V} δ_Σ}$ for larger coupling constants is achieved by adding an additional scaled magnetic term. |
| title | Approximation of Dirac operators with $\boldsymbolδ$-shell potentials in the norm resolvent sense, II. Quantitative results |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2507.01482 |