Superluminal Tunneling of a Relativistic Half-Integer Spin Particle Through a Potential Barrier

TL;DR

This paper demonstrates that relativistic half-integer spin particles can exhibit superluminal tunneling through a potential barrier, with the tunneling time behavior depending on spinor components and barrier parameters.

Contribution

It provides new insights into superluminal tunneling phenomena for relativistic particles, analyzing phase time and spinor component effects in quantum tunneling.

Findings

First spinor components always exhibit superluminal tunneling.

Tunneling time for antiparticles can be negative, indicating superluminal behavior.

Tunneling time approaches zero as barrier height increases.

Abstract

This paper investigates the problem of a relativistic Dirac half integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. In total, the tunneling time always remains positive for particle states while it becomes negative for antiparticle ones. Furthermore, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.