Modified Matthiessen's rule: More scattering leads to less resistance

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