Klein paradox for bosons, wave packets and negative tunnelling times

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.

References in corpus (6)

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• Attosecond angular streaking and tunnelling time in atomic hydrogen
• Non-locality and time-dependent boundary conditions: a Klein-Gordon perspective
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves
• Interference effects in tunnelling of "cat" wave packet states
• Scattering of a scalar relativistic particle by the hyperbolic tangent potential

Cited by in corpus (6)

• Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles
• Numerical simulations of quantum clock for measuring tunneling times
• Relativistic spin-0 particle in a box: bound states, wavepackets, and the disappearance of the Klein paradox
• Beyond the light-cone propagation of relativistic wavefunctions: numerical results
• Computational quantum field theory for fermion pair creation in 2-dimensional curved spacetimes
• Tunneling dynamics of the relativistic Schrodinger/Salpeter equation