Sommaire:

Tunneling in quantum mechanics is a standard illustration of quantum phenomena, distinguished by exponentially decaying solutions within classically forbidden zones. Within the realm of relativistic quantum mechanics, a more intriguing phenomenon than regular quantum tunneling arises – Klein tunneling. This phenomenon involves non-decaying oscillating solutions in classically forbidden areas known as supercritical barriers, characterized by strong fields capable of creating pairs of particles and anti-particles.

In this presentation I will introduce the dynamics governing Klein tunneling exhibited by fermions and bosons in both frameworks of the first quantized and the second quantized theories. In the first quantized theory, the phenomenon is elucidated through the multiple scattering expansion, which converges for fermions but diverges for bosons, providing a partial account of pair creation. Validation of our results is achieved through numerical solutions employing the finite difference method and the split operator method. However, a paradox emerges in the fermionic case, defying resolution within the first quantized framework.

Within the second quantized framework, we use a computational Quantum Field Theory approach in order to account for the pair creation phenomenon. Additionally, we resolve the fermionic paradox by invoking the Pauli blockade. We find that particles do not actually "tunnel" through the supercritical barrier. Instead, it is the modulation of the number densities of created anti-particles (increase for bosons and decrease for fermions) that is responsible for the generation of the "tunneled" particle outside the barrier.

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