Pair Production in time-dependent Electric field at Finite times

Abstract: We investigate the finite-time behavior of pair production from the vacuum by a time-dependent Sauter pulsed electric field. By examining the temporal behavior of the single-particle distribution function, we observe oscillatory patterns in the longitudinal momentum spectrum of the particles at finite times. These oscillations arise due to quantum interference effects resulting from the various dynamical processes/channels leading to the creation of the (quasi-)particle of a given momentum. Furthermore, we derive an approximate and simplified analytical expression for the distribution function at finite times, allowing us to explain these oscillations' origin and behavior. The role of the vacuum polarization function and its counterterm are also discussed in this regard. The transverse momentum spectrum peaked at the nonzero value of the transverse momentum at finite times, which indicates the role of multiphoton transitions in the creation of quasiparticles.