Clemens Staudinger,
"Ground State of Many-Particle Systems in the Hyper-Netted-Chain Theory"
, 2018

Original Titel:

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

Sprache des Titels:

Englisch

Original Kurzfassung:

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.