  We determine the nonlinear time-dependent response of a tracer on a lattice
with randomly distributed hard obstacles as a force is switched on. The
calculation is exact to first order in the obstacle density and holds for
arbitrarily large forces. Whereas, on the impurity-free lattice, the nonlinear
drift velocity in the stationary state is analytic in the driving force,
interactions with impurities introduce logarithmic contributions beyond the
linear regime. The long-time decay of the velocity toward the steady state is
exponentially fast for any finite value of the force, in striking contrast to
the power-law relaxation predicted within linear response. We discuss the range
of validity of our analytic results by comparison to stochastic simulations.
