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Klein's paradox and
the relativistic $\delta$-shell interaction in
$\mathbb{R}^3$
Albert Mas and Fabio Pizzichillo |
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Vol. 11 (2018), No. 3, 705–744
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Abstract |
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Under certain hypotheses of smallness on the regular potential , we prove that the Dirac operator in , coupled with a suitable rescaling of , converges in the strong resolvent sense to the Hamiltonian coupled with a -shell potential supported on , a bounded surface. Nevertheless, the coupling constant depends nonlinearly on the potential ; Klein’s paradox comes into play. |
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Keywords
Dirac operator, Klein's paradox, $\delta$-shell
interaction, singular integral operator, approximation by
scaled regular potentials, strong resolvent convergence
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Mathematical Subject Classification 2010
Primary: 81Q10
Secondary: 35Q40, 42B20, 42B25
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Milestones
Received: 23 January 2017
Revised: 14 September 2017
Accepted: 16 October 2017
Published: 22 November 2017
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Authors |
| Albert Mas | |
| Departament de Matemàtiques i
Informàtica Universitat de Barcelona Barcelona Spain |
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| Fabio Pizzichillo | |
| Basque Center for Applied
Mathematics (BCAM) Bilbao Spain |
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