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2018 Klein's paradox and the relativistic $\delta$-shell interaction in $\mathbb{R}^3$
Albert Mas, Fabio Pizzichillo
Anal. PDE 11(3): 705-744 (2018). DOI: 10.2140/apde.2018.11.705

Abstract

Under certain hypotheses of smallness on the regular potential V, we prove that the Dirac operator in 3, coupled with a suitable rescaling of V, converges in the strong resolvent sense to the Hamiltonian coupled with a δ-shell potential supported on Σ, a bounded C2 surface. Nevertheless, the coupling constant depends nonlinearly on the potential V; Klein’s paradox comes into play.

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Albert Mas. Fabio Pizzichillo. "Klein's paradox and the relativistic $\delta$-shell interaction in $\mathbb{R}^3$." Anal. PDE 11 (3) 705 - 744, 2018. https://doi.org/10.2140/apde.2018.11.705

Information

Received: 23 January 2017; Revised: 14 September 2017; Accepted: 16 October 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 06820937
MathSciNet: MR3738260
Digital Object Identifier: 10.2140/apde.2018.11.705

Subjects:
Primary: 81Q10
Secondary: 35Q40 , 42B20 , 42B25

Keywords: $\delta$-shell interaction , approximation by scaled regular potentials , Dirac operator , Klein's paradox , singular integral operator , strong resolvent convergence

Rights: Copyright © 2018 Mathematical Sciences Publishers

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