Ground State of Many-Particle Systems in the Hyper-Netted-Chain Theory

A deeper understanding of the correlated behaviour of charged particles is nowadays cru- cial for advances in the fields of quantum electronics, nanotechnology and in physics in general. Currently under extensive experimental study are ultracold charged boson gases. Electrons, as realised in two-dimensional (2D) conducting layers and a hot topic for the past few decades, remain an even higher challenge due to Pauli exclusion. This work merges both issues. I calculate ground state properties of multi-component bulk bosons as well as spin polarised 3D and 2D electron systems. Emphasis is put on the pair distribution function g(r) and the static structure factor S(k), which entirely determine the structure of a many-particle system in real and momentum space, respectively. These functions allow the calculation of the energy, laying the foundation to also treat phase transitions. A most elaborate way to access g(r) are advanced quantum Monte-Carlo (MC) simulations. Here I choose a different path, which puts the weight on computational speed, while simultan- eously maintaining reasonably high accuracy. This allows to cover a wide range of systems with different densities and spin polarisations in a fraction of the time a MC calculation takes. The employed approach, developed by Davoudi and Asgari (2003), is based on the "Hyper-Netted-Chain" theory, originally addressing classical liquids. After confirming the results for bulk electrons, I extend the formalism to 2D systems. My results are in perfect agreement with those of MC for high densities and somewhat less satisfactory in the dilute (strongly correlated) case. Finally, I present the first spin-resolved calculations for 2D systems with finite thickness, offering a more realistic description of semiconductor quantum wells.