Emergent Time Scales in the Momentum Spectrum of Non-Perturbative e−e+ pair production

We study the real-time dynamics of vacuum electron–positron pair production in a time-dependent Sauter-type electric field, focusing on the emergence of characteristic time scales associated with particle formation. From the time evolution of the transverse momentum distribution, we extract three distinct time scales corresponding to the onset of spectral deformation, the reorganization of interference structures, and the final freeze-in of real particles. We show that these time scales depend on the external field parameters, with the peak field strength governing the dynamics and the pulse duration providing a secondary control. Our results provide a time-resolved characterization of transverse momentum formation and offer new insight into non-equilibrium dynamics in strong-field quantum electrodynamics(SFQED).