Critical Schwinger Pair Production

We investigate Schwinger pair production in spatially inhomogeneous electric backgrounds. A critical point for the onset of pair production can be approached by fields that marginally provide sufficient electrostatic energy for an off-shell long-range electron-positron fluctuation to become a real pair. Close to this critical point, we observe features of universality which are analogous to continuous phase transitions in critical phenomena with the pair-production rate serving as an order parameter: electric backgrounds can be subdivided into universality classes and the onset of pair production exhibits characteristic scaling laws. An appropriate design of the electric background field can interpolate between power-law scaling, essential Berezinskii-Kosterlitz-Thouless-type scaling, and a power-law scaling with log corrections. The corresponding critical exponents only depend on the large-scale features of the electric background, whereas the microscopic details of the background play the role of irrelevant perturbations not affecting criticality.