Time Scales in Dynamical Sauter–Schwinger Pair Creation: Dependence on Transverse Momentum

We investigate the dynamics of particle creation in a time-dependent, spatially uniform Sauter pulsed electric field by analyzing the evolution of the one-particle momentum distribution function. This quantity provides key insights into the non-perturbative process of electron–positron pair production in strong-field quantum electrodynamics. The longitudinal momentum spectrum of the created particles exhibits rich features, including spectral splitting and oscillatory behavior, particularly around the time when the electric field approaches zero. These oscillations can be attributed to quantum interference effects during the dynamical evolution. By examining the temporal evolution of the spectrum, we identify three distinct characteristic time scales associated with key spectral transitions, which depend on the transverse momentum p⊥. We find out approximate expressions for the relevant time scales as functions of p⊥, the pulse duration τ, and the field strength E0, offering a clearer understanding of the interplay between field parameters and the dynamics of pair production.