Interplay between two mechanisms of resistivity

TL;DR

This paper challenges the empirical Matthiessen rule by demonstrating that resistivity mechanisms are correlated and that zero dissipation limits do not commute, using a simple model to clarify these fundamental issues.

Contribution

It introduces a model illustrating the correlation between resistivity mechanisms and the non-commutativity of zero dissipation limits, highlighting limitations of the Matthiessen rule.

Findings

Matthiessen rule can be misleading due to correlations.

Limits of zero electric field and zero dissipation do not commute.

Variational principles are important for non-equilibrium steady states.

Abstract

Mechanisms of resistivity can be divided into two basic classes: one is dissipative (like scattering on phonons) and another is quasi-elastic (like scattering on static impurities). They are often treated by the empirical Matthiessen rule, which says that total resistivity is just the sum of these two contributions, which are computed separately. This is quite misleading for two reasons. First, the two mechanisms are generally correlated. Second, computing the elastic resistivity alone masks the fundamental fact that the linear-response approximation has a vanishing validity interval at vanishing dissipation. Limits of zero electric field and zero dissipation do not commute for the simple reason that one needs to absorb the Joule heat quadratic in the applied field. Here, we present a simple model that illustrates these two points. The model also illuminates the role of variational principles for non-equilibrium steady states.