Nonadiabatic quantum Vlasov equation in spinor QED

TL;DR

This paper derives a nonadiabatic quantum Vlasov equation for spinor QED, compares it with the adiabatic case, and analyzes the dynamics of particle pair production, revealing unique oscillation behaviors.

Contribution

It introduces a new nonadiabatic quantum Vlasov equation for spinor QED and explores its relation to the adiabatic case through three methods, providing new insights into pair production dynamics.

Findings

Oscillation periods of distribution functions equal pi divided by total energy.

Momentum distributions exhibit novel out-of-phase oscillations.

Comparison with scalar QED reveals distinct oscillation behaviors.

Abstract

The nonadiabatic quantum Vlasov equation in spinor QED is derived, and its relation to the well-known adiabatic one is established by three methods. One is by an explicitly analytical expression, the second is by the Dirac equation in the V gauge, and the last is by introducing a turn-off electric field. Wherein what the first two of them are given is an instantaneous relation. Moreover, the time evolution of the distribution function for a specific momentum and the momentum distribution of created particle pairs after turning off the electric field are calculated and compared with those in scalar QED. It is found that both the oscillation periods of the distribution functions in spinor and scalar QED equal pi divided by the total energy of a particle after the electric field is turned off. The momentum distributions in spinor and scalar QED show a novel oscillation and out-of-phase behavior that cannot be explained by the Stokes phenomenon. These findings will further deepen our understanding of the quantum Vlasov equation and its application in vacuum pair production.