Invariance principles in the theory and computation of transport coefficients.

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, , 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 , gauge invariance also sheds new light onto the mechanisms of charge transport in ionic conductors. The second principle, , 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.