Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses

Particle production due to external fields (electric, chromoelectric, or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with substructure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. We give a simple quantitative explanation of the recently computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of e(+)e(-) pairs produced from vacuum subjected to a time-dependent electric field with subcycle laser pulse structure. This approach also explains naturally why for spinor and scalar QED these oscillations are out of phase.