  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 necessarily 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 symmetric
superfluid-Mott insulator transition of bosons.
