A strange weak value in spontaneous pair productions via a supercritical step potential

TL;DR

This paper explores how weak values, typically used in measurement theory, can describe the group velocity during spontaneous pair production in a Dirac system, revealing superluminal weak values linked to supercritical potentials.

Contribution

It introduces the concept of weak values as physical quantities in a relativistic quantum process, providing a quantitative explanation for pair production via supercritical potentials.

Findings

Weak values can describe group velocities in Dirac particles.

Supercritical potentials correspond to superluminal weak values.

Weak values offer insight into pair production mechanisms.

Abstract

We consider a case where a weak value is introduced as a physical quantity rather than an average of weak measurements. The case we treat is a time evolution of a particle by 1+1 dimensional Dirac equation. Particularly in a spontaneous pair production via a supercritical step potential, a quantitative explanation can be given by a weak value for the group velocity of the particle. We also show the condition for the pair production (supercriticality) corresponds to the condition when the weak value takes a strange value (superluminal velocity).