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, 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.

arXiv comment14 pages, 7 figures

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• Thermal conductivity of Li${}_3$PS${}_4$ solid electrolytes with ab initio accuracy
• Self-interaction and transport of solvated electrons in molten salts
• Seebeck coefficient of liquid water from equilibrium molecular dynamics
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• Investigating finite-size effects in molecular dynamics simulations of ion diffusion, heat transport, and thermal motion in superionic materials
• Green and Kubo forge the arrow of time
• Topology, oxidation states, and charge transport in ionic conductors
• Stochastic perturbation theory: a prequel to Reptation Quantum Monte Carlo