Less is more: more scattering leading to less resistance

TL;DR

This paper investigates how dilute impurities affect transport in integrable systems, revealing that adding more impurities can sometimes enhance transport, contrary to traditional expectations, especially in systems with anomalous diffusion.

Contribution

It demonstrates that impurity scattering in anomalous transport systems does not follow Matthiessen's rule and uncovers a regime where more impurities lead to increased transport.

Findings

Diffusion constant exhibits a nontrivial power-law dependence on impurity density.

Adding impurities can increase transport in certain high-density regimes.

Traditional additive scattering assumptions do not hold in anomalous transport scenarios.

Abstract

We study the breaking of integrability by a finite density of dilute impurities, specifically the emerging diffusive transport. Provided the distance between impurities (localized perturbations) is large, one would expect that the scattering rates are additive, and therefore, the resistivity is proportional to the number of impurities (the so-called Matthiessen's rule). We show that this is, in general, not the case. If transport is anomalous in the original integrable system without impurities, the diffusion constant in the non-integrable system at low impurity density gets a nontrivial power-law dependence on the impurity density, with the power being determined by the dynamical scaling exponent of anomalous transport. We also find a regime at high impurity density in which, counterintuitively, adding more impurities to an already diffusive system increases transport rather than decreases it.