Self-consistent dielectric formalism scheme for the paramagnetic electron gas under warm dense matter conditions

The present thesis aims to further a somewhat unexplored area of Warm Dense Matter (WDM) physics through the use of tools developed within the dielectric formalism. WDM is an exotic form of matter with densities close to the solid state and temperatures of several eV. The accurate description of WDM is important for the understanding of the physics of dense astrophysical objects (gas giants, brown dwarfs, neutron stars) and of the initial phase of inertial confinement fusion. This necessitates an accurate knowledge of the exchange-correlation free energy functional for weakly non-ideal Quantum One-Component plasmas (qOCP). The later has been recently obtained by modern Quantum Monte Carlo (QMC) simulation techniques that alleviate the notorious fermion sign problem. Currently, pure theoretical schemes of the qOCP under WDM conditions significantly lag behind QMC simulations and this will be the main issue addressed in this thesis. In this project, we will investigate a dielectric formalism scheme tailor made for weak correlations that treats quantum mechanical effects on the random phase approximation level and satisfies the compressibility sum rule exactly by construction. More precisely, it is a self-consistent dielectric scheme for the finite temperature qOCP that is based on the Vashishta-Singwi (VS) closure of the classical BBGKY hierarchy.