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

TL;DR

This paper analyzes quantum transport in a free fermion lattice with a localized defect after a quantum quench, deriving exact asymptotics for particle density and current using a new analytical method.

Contribution

It introduces a rigorous analytical approach to compute large time and distance asymptotics in non-interacting quantum transport with defects, confirming semiclassical predictions.

Findings

Semiclassical approach matches exact asymptotics away from the defect

Derived exact profiles of particle density and current

Formulated general expressions in terms of defect scattering properties

Abstract

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.