Particle self-bunching in the Schwinger effect in spacetime-dependent   electric fields
  Non-perturbative electron-positron pair creation (Schwinger effect) is studied based on the equal-time Wigner formalism in 1+1 dimensions. An ab initio calculation of the Schwinger effect in the presence of a simple space- and time-dependent electric field pulse is performed for the first time, allowing for the calculation of the time evolution of observable quantities such as the charge density, the particle number density or the total number of created particles. We predict a new self-bunching effect of charges in phase space due to the spatial and temporal structure of the pulse. 
Florian Hebenstreit, Reinhard Alkofer, Holger Gies
hep-ph hep-th quant-ph