Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909806067974144 |
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| author | Benhellal, Badreddine Pankrashkin, Konstantin |
| author_facet | Benhellal, Badreddine Pankrashkin, Konstantin |
| contents | We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the interaction may result in a new interval of essential spectrum. The position and the length of the interval are explicitly controlled by the coupling constants and the principal curvatures of the surface. This effect is completely new compared to lower dimensional critical situations or special geometries considered up to now, in which only a single new point in the essential spectrum was observed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10264 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions Benhellal, Badreddine Pankrashkin, Konstantin Spectral Theory Analysis of PDEs 35Q40 (Primary) 47A10, 58J40 (Secondary) We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the interaction may result in a new interval of essential spectrum. The position and the length of the interval are explicitly controlled by the coupling constants and the principal curvatures of the surface. This effect is completely new compared to lower dimensional critical situations or special geometries considered up to now, in which only a single new point in the essential spectrum was observed. |
| title | Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions |
| topic | Spectral Theory Analysis of PDEs 35Q40 (Primary) 47A10, 58J40 (Secondary) |
| url | https://arxiv.org/abs/2211.10264 |