Invariance principles in the theory and computation of transport coefficients

TL;DR

This paper discusses two invariance principles—gauge and convective invariance—that simplify the calculation of transport coefficients in complex systems, enabling more accurate and efficient molecular dynamics simulations.

Contribution

It introduces and elaborates on two invariance principles that make transport coefficient calculations independent of microscopic definitions, enhancing computational methods.

Findings

Gauge invariance enables defining heat conductivity from density-functional theory.

Topological atomic oxidation states provide new insights into charge transport.

Spectral analysis methods improve accuracy of transport coefficients from short simulations.

Abstract

In this work we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transported (energy, momentum, mass, charge). The first such principle, gauge invariance, allows one to define a quantum adiabatic energy current from density-functional theory, from which the heat conductivity can be uniquely defined and computed using equilibrium ab initio molecular dynamics. When combined with a novel topological definition of atomic oxidation states, gauge invariance also sheds new light onto the mechanisms of charge transport in ionic conductors. The second principle, convective invariance, allows one to extend the analysis to multi-component systems. These invariance principles can be combined with new spectral analysis methods for the current time series to be fed into the Green-Kubo formula to obtain accurate estimates of transport coefficients from relatively short molecular dynamics simulations.