Solving the Boltzmann equation beyond Relaxation Time Approximation in the Warm Dense Matter regime

The warm and dense matter (WDM) regime is of great interest in various areas of science, including inertial confinement fusion of which it is a transient stage and astrophysics, as the centers of large planets are believed to be in a WDM state. The challenging nature of modeling this state of matter comes from it having too high a temperature for solid-state physics principles to apply, but being too dense to fall in the range of plasma physics. This makes obtaining its properties, such as the absorption or electrical conductivity both theoretically and numerically challenging.

Resorting to the average atom approximation allows to speed up the calculations. However, a well-known problem inherent to this approximation is the divergence of the conductivity at low frequencies, when computed using the Kubo-Greenwood formalism. Other approaches should be used to tackle this problem. Among them, there is the Boltzmann transport equation in the Relaxation Time Approximation (RTA).

However, few previous works have addressed the issue of the accuracy of this approximation. In this work, we explore different solutions to Boltzmann's equation, both theoretical and numerical, with collision operators constructed using average atom wave functions. We therefore go beyond RTA. We calculate transport properties, such as frequency-dependent electrical conductivity, and compare them with a calculation in the RTA approximation, as well as with ab initio calculations relying on the Kubo-Greenwood approach.