https://doi.org/10.1140/epjb/s10051-021-00152-5
Regular Article - Computational Methods
Invariance principles in the theory and computation of transport coefficients
1
COSMO–Laboratory of Computational Science and Modelling, IMX, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
2
SISSA–Scuola Internazionale Superiore di Studi Avanzati, 34136, Trieste, EU, Italy
3
CNR-IOM DEMOCRITOS Simulation Center, SISSA, 34136, Trieste, EU, Italy
Received:
4
May
2021
Accepted:
5
July
2021
Published online:
3
August
2021
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.
© The Author(s) 2021
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