  We study quantum transport after an inhomogeneous quantum quench in a free
fermion lattice system in the presence of a localised defect. Using a new
rigorous analytical approach for the calculation of large time and distance
asymptotics of physical observables, we derive the exact profiles of particle
density and current. Our analysis shows that the predictions of a semiclassical
approach that has been extensively applied in similar problems match exactly
with the correct asymptotics, except for possible finite distance corrections
close to the defect. We generalise our formulas to an arbitrary non-interacting
particle-conserving defect, expressing them in terms of its scattering
properties.
