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Open Quantum Systems Decoherence

The role of the slope of `realistic' potential barriers in preventing relativistic tunnelling in the Klein zone

arXiv
Authors: Paolo Christillin, Emilio d'Emilio

Year

2007

Paper ID

49959

Status

Preprint

Abstract Read

~2 min

Abstract Words

111

Citations

N/A

Abstract

The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e. supporting an infinite electric field), of height U> E + m - due to the many-body nature of the Dirac equation evidentiated by the Klein paradox - has been widely studied. We exploit here the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunnelling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelenght of the particle - the latter circumstance being hardly escapable in most realistic cases.

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  • The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0706.2266 [2] arXiv https://arxiv.org/abs/0706.2266 [3] Publisher https://arxiv.org/abs/0706.2266

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