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arXiv · 2107.09374

Klein paradox for bosons, wave packets and negative tunnelling times

X. Gutiérrez de la Cal·M. Alkhateeb·M. Pons·A. Matzkin·D. Sokolovski
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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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X. Gutiérrez de la Cal, M. Alkhateeb, M. Pons, A. Matzkin, D. Sokolovski. 2021-07-20. Klein paradox for bosons, wave packets and negative tunnelling times. https://doi.org/10.1038/s41598-020-76065-7

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