In this work some many-body properties of isolated mesoscopic rings are investigated.
Second quantization and tight-binding models for systems of spinless
fermions and fermions with spin are used to derive an expression for the persistent
current. The results obtained for non-interacting systems are in satisfactory
agreement with both experimental measurements and other theoretical results.
Then a Coulomb repulsion is considered for a system of interacting fermions and
a variational approach is adopted. We attempt to improve the description of
the system by introducing rotations of the spin-quantization axis on each site.
Then we go on to show how the emergent Hartree–Fock equations may be treated,
what kind of effects have to be considered and how the trial wave functions can
be chosen accordingly.
A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.