arXiv subjects

X. Gutierrez de la Cal

Publications and source records attributed to X. Gutierrez de la Cal.

3 recordsLinked to original sources

arXiv2026

Relativistic Quantum Field Theory Approach to Wavepacket Tunneling: Lack of Superluminal Transmission

We investigate relativistic wavepacket dynamics for an electron tunneling through a potential barrier employing space-time resolved solutions to relativistic quantum field theory (QFT) equations. We prove by linking the QFT property of micro-causality to the wavepacket behavior that the tunneling dynamics is fully causal, precluding instantaneous or superluminal effects that have recently been reported in the literature. We illustrate these results by performing numerical computations for an electron tunneling through a potential barrier for standard tunneling as well for Klein tunneling. In all cases (Klein tunneling \ or regular tunneling across a standard or a supercritical potential) the transmitted wavepacket remains in the causal envelope of the propagator, even when its average position lies ahead of the average position of the corresponding freely propagated wavepacket.

quant-ph↗

arXiv2023

Beyond the light-cone propagation of relativistic wavefunctions: numerical results

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schrödinger) equation or for Klein-Gordon and Dirac wavefunctions defined in the Foldy-Wouthuysen representation. In this work we investigate quantitatively the degree of non-causality for free propagation for different types of wavepackets all having initially a compact spatial support. In the studied examples we find that non-causality appears as a small transient effect that can in most cases be neglected. We display several numerical results and discuss the fundamental and practical consequences of our findings concerning this peculiar dynamical feature.

quant-ph↗

arXiv2021

Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles

We investigate wavepacket dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of the usual connection formulas for the scattering basis functions. In a time-dependent formulation, the divergent character of the MSE naturally accounts for charge creation at the barrier boundaries. In the Dirac case, the MSE converges and no charge is created. We show that this time-dependent charge behavior dynamics can adequately explain the Klein paradox in a first quantized setting. We further compare our semi-analytical wavepacket approach to exact finite-difference solutions of the relativistic wave equations.

quant-ph↗