Non-equilibrium quantum transport in presence of a defect: the non-interacting case

Understand

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.