Spectral methods for the analysis of transport phenomena in electronic insulators

Understanding and controlling heat and charge transport is central to the design of efficient thermoelectric materials and solid-state ionic conductors. However, the prediction of transport coefficients from equilibrium molecular dynamics remains challenging, requiring long simulations and robust statistical tools. I will present a unified framework based on spectral analysis of current time series, enabling the accurate computation of the full Onsager matrix—including both diagonal and off-diagonal transport coefficients—from a single statistical model. The method is demonstrated on molten salts, liquid water, and the Li₃PS₄ solid-state electrolyte. Building on this, I will explore the microscopic origins of thermal transport in the Li₃ClO antiperovskite, where a combination of ab initio, machine-learning, and empirical force-field simulations reveals the key roles of anharmonicity and ionic diffusion in characterizing thermal conductivity. Finally, I will briefly turn to the case of SiGe thermoelectrics, showing how spatially correlated mass disorder can strongly suppress lattice heat transport and provide a viable pathway to enhancing thermoelectric performance through engineered disorder.