Using numerical solutions to quantum field theory, the creation of boson-antiboson pairs from the vacuum under a very strong localized external electric field is explored. The simulations reveal that the initial linear increase of the number of particles turns into an exponential growth. This self-amplification can be understood as the result of the interaction of the previously generated particles with the creation process. While the number of particles keeps increasing, the spatial shape of the (normalized) charge density of the created particles reaches a universal form that can be related to the bound states of the supercritical potential well. We accompany the space-time resolved quantum field theoretical simulations with a model calculation that allows us to interpret the numerical simulations in terms of simple classical mechanical concepts.
Wagner, R E.; Ware, M R.; Su, Q; and Grobe, Rainer, "Exponential enhancement of field-induced pair creation from the bosonic vacuum" (2010). Faculty publications – Physics. Paper 23.