Full counting statistics of Schwinger pair production and annihilation

TL;DR

This paper derives a comprehensive statistical description of particle-antiparticle pair production and annihilation in the Schwinger effect under time-dependent electric fields, revealing effects of quantum statistics and medium interactions.

Contribution

It introduces a novel formula for the probability distribution of pairs produced and annihilated, connecting Schwinger physics with mesoscopic transport techniques.

Findings

Pair production is enhanced for scalars and suppressed for spinors due to quantum statistics.

The formula captures generalized trinomial and bidirectional Poisson statistics.

Both pair creation and annihilation processes are quantitatively described.

Abstract

We study the probability distribution of the number of particle and antiparticle pairs produced via the Schwinger effect when a uniform but time-dependent electric field is applied to noninteracting scalars or spinors initially at a thermodynamic equilibrium. We derive the formula for the characteristic function by employing techniques in mesoscopic physics, reflecting a close analogy between the Schwinger effect and mesoscopic tunneling transports. In particular, we find that the pair production in a medium is enhanced (suppressed) for scalars (spinors) due to the Bose stimulation (Pauli blocking). Furthermore, in addition to the production of accelerated pairs by the electric field, the annihilation of decelerated pairs is found to take place in a medium. Our formula allows us to extract the probability distributions in various situations, such as those obeying the generalized trinomial statistics for spin-momentum resolved counting and the bidirectional Poisson statistics for spin-momentum unresolved counting.