Year: 2025
Type: article
Abstract: Recent interest in the studies of structured states obtained in relativistic electron beams has highlighted the use of two alternative descriptions, each based on a different wavefunction and the related space-time density. Although both wavefunctions obey the Dirac equation (one directly and the other through a Foldy-Wouthuysen transformation) they lead to different dynamics and properties, such as the presence or absence of spin-orbit interactions. In this work we investigate wavepacket dynamics for the Klein-Gordon equation, which displays the same ambiguity regarding the choice of different densities, in a setting involving Klein tunneling across a series of supercritical potential barriers. Relying on the superradiant character of this setting, we obtain solutions to the wavepacket dynamics indicating that the density based on a Foldy-Wouthuysen transformation of the wavefunction can be locally amplified outside the light-cone. In principle, the exponential increase of the charge due to the field inhomogeneities can lead to an arbitrarily large amplification over macroscopic distances. These results question the interpretation of the Foldy-Wouthuysen density as a fundamentally correct probability or charge density.
Source: Physical Review A
DOI: 10.1103/d38q-h3qw
Authors: F. Daem, A. Matzkin
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410765267