Nuclear quantum effects in thermal conductivity from centroid molecular dynamics

TL;DR

This paper demonstrates that centroid molecular dynamics can accurately compute the thermal diffusivity and conductivity of quantum liquids like para-hydrogen and helium, aligning well with experimental data across temperatures.

Contribution

It introduces a practical approach combining CMD and path integral MD to calculate quantum thermal properties, capturing low-temperature effects previously missed.

Findings

CMD accurately predicts thermal conductivity of para-hydrogen.

Method captures decrease in conductivity at low temperatures.

Results agree with experimental measurements for helium and hydrogen.

Abstract

We show that the centroid molecular dynamics (CMD) method provides a realistic way to calculate the thermal diffusivity $a=\lambda/\rho c_{\rm V}$ of a quantum mechanical liquid such as para-hydrogen. Once $a$ has been calculated, the thermal conductivity can be obtained from $\lambda=\rho c_{\rm V}a$, where $\rho$ is the density of the liquid and $c_{\rm V}$ is the constant-volume heat capacity. The use of this formula requires an accurate quantum mechanical heat capacity $c_{\rm V}$, which can be obtained from a path integral molecular dynamics simulation. The thermal diffusivity can be calculated either from the decay of the equilibrium density fluctuations in the liquid or by using the Green-Kubo relation to calculate the CMD approximation to $\lambda$ and then dividing this by the corresponding approximation to $\rho c_{\rm V}$. We show that both approaches give the same results for liquid para-hydrogen and that these results are in good agreement with experimental measurements of the thermal conductivity over a wide temperature range. In particular, they correctly predict a decrease in the thermal conductivity at low temperatures -- an effect that stems from the decrease in the quantum mechanical heat capacity and has eluded previous para-hydrogen simulations. We also show that the method gives equally good agreement with experimental measurements for the thermal conductivity of normal liquid helium.