Analysing Warm Dense Matter through the usage of dielectric formalism

Warm dense matter (WDM) concerns partially ionized high energy density matter at near-solid mass densities and at temperatures exceeding 10000K. WDM lies at the intersection of condensed matter physics, plasma physics and dense liquid physics. WDM naturally occurs in dense astrophysical objects (giant gas planet interiors, brown dwarfs, neutron star crusts) and emerges on the path to inertial confinement fusion. A prerequisite for an improved understanding of WDM is the accurate description of the uniform electron fluid (UEF) at finite temperatures and arbitrary degeneracy. This is a formidable task by itself, given the non-trivial interplay of strong Coulomb coupling, quantum diffraction, exchange effects and thermal excitations. This is reflected in the lack of small parameters that forbid perturbative expansions around the non-interacting system, the ground state limit, the high-temperature limit or the perfect Wigner crystal.

Ab initio quantum Monte Carlo (QMC) methods can provide very accurate results for the UEF, but computational costs prevent their application in the full phase diagram. The self-consistent dielectric formalism constitutes a mature, promising and versatile theoretical tool for UEF studies. It is based on the quantum fluctuation-dissipation theorem, the zero-frequency moment sum rule and a closure expression for the dynamic or static local field correction. Depending on the closure expression, there are different schemes of the dielectric formalism that are based on semi- classical kinetic theory, quantum kinetic theory or integral equation theory. This particular presentation will focus mainly on the computational implementation of a specific closure expression within the Bogoliubov-Born-Green Kirkwood-Yvon (BBGKY) hierarchy called the Vashishta-Singwi (VS) closure.