Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense to the Hamiltonian coupled with a $\delta$-shell potential supported on $\Sigma$...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/741 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/741 |
| Access Level: | acceso abierto |
| Palabra clave: | Dirac operator Klein's Paradox $\delta$-shell interaction singular integral operator approximation by scaled regular potentials strong resolvent convergence |
| Sumario: | Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense to the Hamiltonian coupled with a $\delta$-shell potential supported on $\Sigma$, a bounded $C^2$ surface. Nevertheless, the coupling constant depends non-linearly on the potential $\mathbf{V}$: the Klein's Paradox comes into play. |
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