# Accurate thermal conductivities from optimally short molecular dynamics simulations

## TL;DR

This paper presents a novel method to accurately compute thermal conductivities from short molecular dynamics simulations using Green-Kubo theory and cepstral analysis, significantly reducing simulation time needed.

## Contribution

The authors introduce a new unbiased, consistent approach leveraging spectral analysis to estimate transport coefficients from short MD trajectories, enabling practical quantum simulations.

## Key findings

- Achieves ~10% accuracy with simulations of a few hundred picoseconds.
- Validates method on liquids and solids, including Ar, H2O, MgO, and a-SiO2.
- Reduces computational cost for transport property evaluation.

## Abstract

The evaluation of transport coefficients in extended systems, such as thermal conductivity or shear viscosity, is known to require impractically long simulations, thus calling for a paradigm shift that would allow to deploy state-of-the-art quantum simulation methods. We introduce a new method to compute these coefficients from optimally short molecular dynamics simulations, based on the Green-Kubo theory of linear response and the cepstral analysis of time series. Information from the full sample power spectrum of the relevant current for a single and relatively short trajectory is leveraged to evaluate and optimally reduce the noise affecting its zero-frequency value, whose expectation is proportional to the corresponding conductivity. Our method is unbiased and consistent, in that both the resulting bias and statistical error can be made arbitrarily small in the long-time limit. A simple data-analysis protocol is proposed and validated with the calculation of thermal conductivities in the paradigmatic cases of elemental and molecular fluids (liquid Ar and H$_2$O) and of crystalline and glassy solids (MgO and a-SiO$_2$). We find that simulation times of one to a few hundred picoseconds are sufficient in these systems to achieve an accuracy of the order of 10% on the estimated thermal conductivities.