Electron-phonon thermalization of warm dense beryllium from first-principles

Understanding the thermalization processes in warm dense matter (WDM) are essential to improving the modeling, design, and understanding of high energy density physics (HEDP) experiments. In this work, we study electron-phonon (e-ph) thermalization in isochorically heated solid-density beryllium using first-principles methods. Density functional theory (DFT) and density functional perturbation theory (DFPT) are used to obtain e-ph matrix elements that are then used as inputs to solve the electron Boltzmann transport equation (BTE). We solve the BTE with the software PERTURBO, which allows us to determine how out of equilibrium electrons and phonons populations equilibrate over time, with sub-femtosecond resolution. In our study, we consider how electrons with initial electronic temperatures from ~0.1-1 eV thermalize to the phonon temperature of 400 K due to e-ph scattering. While the initial and final distributions obey Fermi-Dirac statistics by construction, we observe that the intermediate distrubutions are non-thermal. We use the results from these simulations to determine the time scales of e-ph equilibration, model effective electronic temperatures for intermediate steps, and determine energy transfer rates. These results will benchmark and reveal the limitations of the two-temperature models that are often used in HEDP simulations.