Klein paradox for bosons, wave packets and negative tunnelling times
X. Gutiérrez de la Cal, M. Alkhateeb, M. Ll. Pons +2 more
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.
arXiv:2107.09374•Scientific Reports•Nov 5, 2020•9 citations