Invariance principles of transport coefficients and their application to superionic conductors

The Green-Kubo theory of linear response makes it possible to extract transport coefficients, like diffusion coefficients or the electric and thermal conductivities of a material, from the time correlation functions of properly defined fluxes that can be sampled via equilibrium molecular dynamics simulations [1]. In my talk I will start by summarizing some recent advances on this topic. In particular, I will discuss some invariance principles according to which the transport coefficients are largely independent of the definitions of atomic quantities [2,3]. I will then show how to obtain accurate estimates of the thermal conductivity and its uncertainty from relatively short trajectories, thanks to the multivariate cepstral analysis of the time series of the fluxes involved in transport processes [4,5]. I will showcase these theoretical and data analysis tools for the paradigmatic examples of superionic water [6] and a typical Li-ion solid-state conductor, Li3ClO [7]. I shall conclude with a thorough investigation of finite-size effects in the ionic dynamics and thermal transport of superionic conductors [8].


[1] Kubo, R., Yokota, M., & Nakajima, S. (1957). Statistical-mechanical theory of irreversible processes. II. Response to thermal disturbance. Journal of the Physical Society of Japan, 12(11), 1203-1211.
[2] Marcolongo, A., Umari, P., & Baroni, S. (2016). Microscopic theory and quantum simulation of atomic heat transport. Nature Physics, 12(1), 80-84.
[3] Grasselli, F., & Baroni, S. (2021). Invariance principles in the theory and computation of transport coefficients. The European Physical Journal B, 94(8), 1-14.
[4] Ercole, L., Marcolongo, A., & Baroni, S. (2017). Accurate thermal conductivities from optimally short molecular dynamics simulations. Scientific reports, 7(1), 1-11.
[5] Bertossa, R., Grasselli, F., Ercole, L., & Baroni, S. (2019). Theory and numerical simulation of heat transport in multicomponent systems. Physical Review Letters, 122(25), 255901.
[6] Grasselli, F., Stixrude, L., & Baroni, S. (2020). Heat and charge transport in H2O at ice-giant conditions from ab initio molecular dynamics simulations. Nature Communications 11, 3605.
[7] Pegolo, P., Baroni, S., & Grasselli, F. (2022). Temperature-and vacancy-concentration-dependence of heat transport in Li3ClO from multi-method numerical simulations. npj Computational Materials, 8(1), 1-9.
[8] Grasselli, F. (2022). Investigating finite-size effects in molecular dynamics simulations of ion diffusion, heat transport, and thermal motion in superionic materials. The Journal of Chemical Physics, 156(13), 134705.

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