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Klein paradox for bosons, wave packets and negative tunnelling times

Authors
  • Gutiérrez de la Cal, X.1
  • Alkhateeb, M.2
  • Pons, M.3
  • Matzkin, A.2
  • Sokolovski, D.1, 4
  • 1 Universidad del País Vasco, UPV/EHU, Leioa, Spain , Leioa (Spain)
  • 2 CY Cergy Paris Université, Cergy-Pontoise cedex, 95302, France , Cergy-Pontoise cedex (France)
  • 3 Universidad del País Vasco, UPV-EHU, Bilbao, Spain , Bilbao (Spain)
  • 4 IKERBASQUE, Basque Foundation for Science, Bilbao, 48011, Spain , Bilbao (Spain)
Type
Published Article
Journal
Scientific Reports
Publisher
Springer Nature
Publication Date
Nov 05, 2020
Volume
10
Issue
1
Identifiers
DOI: 10.1038/s41598-020-76065-7
Source
Springer Nature
License
Green

Abstract

We analyse a little known aspect of the Klein paradox. A Klein–Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein–Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barrier’s height is enhanced yet remains finite.

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