Spin-Density Functionals of a Two-Dimensional Fermionic Gas of Dipolar Atoms: Thomas-Fermi-Dirac Treatment

Abstract

In this thesis, the spin-density functionals are derived for the ground-state energies of a two-dimensional gas of neutral atoms with magnetic-dipole interaction, in the Thomas- Fermi-Dirac approximation. For many atoms in a harmonic trap, we discuss the numerical procedures necessary to solve for the single-particle density and spin-imbalance density, in dependence on the interaction strength and the external magnetic field. We also give analytical solutions in the weak-interaction limit that is relevant for experiments.