Non-linear quantum critical transport and the Schwinger Mechanism

Scaling arguments imply that quantum critical points exhibit universal non-linear responses to external probes. We investigate the origins of such non-linearities in transport, which is especially problematic since the system is neccessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism---the production of carriers from the vacuum by the applied field--- which is then balanced against a scattering rate which is itself set by the field. We show by explicit computation how this works for the case of the superfluid-Mott insulator transition of bosons at commensurate fillings.