Longitudinal Momentum Spectra of pair created in a pulsed field at finite times: Are Oscillations "Real"

We discuss the mechanism of production of electron-positron pairs from the vacuum in a time-varying, spatially uniform pulsed electric field. We analytically compute the probability of $(e^+ e^-) $pair production in momentum space using the exact solution of the one-particle time-dependent Dirac equation and compare the result with quantum kinetic theory (QKT). Both approaches allow us to study the particle momentum spectrum at any instant in time and can potentially unveil valuable information regarding quantum non-equilibrium physics. We analyze both approaches' momentum spectra of the created particles at any instant. We observe a multi-profile structure in the LMS. This multi-profile structure clearly illustrates the quantum interference effects associated with pair production. It is worth noting that both approaches exhibit quantum interference patterns at finite times, manifested as oscillations observed in the LMS. We highlight that this quantum signature is a universal behavior seen in the momentum spectra at finite times, where the electric field is nearly zero.