Full counting statistics of Schwinger pair production and annihilation

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.

Automated summary

This study investigates the probability distribution of particle and antiparticle pairs produced via the Schwinger effect under the influence of a time-dependent electric field. The findings suggest that pair production is enhanced or suppressed in a medium for scalars or spinors respectively, due to Bose stimulation or Pauli blocking. Additionally, the annihilation of decelerated pairs is observed, along with the extraction of probability distributions in various scenarios using specialized statistics.