Gaps, Traps and Lattices - Correlations in Small Quantum Systems

Abstract: This dissertation investigates properties of two-dimensional many-body systems. Studies are performed using the Spin-Density Functional Theory with the Local Spin-Density Approximation, and numerical exact diagonalization. The properties studied include symmetry-breaking states in few-electron quantum dots, gaps in confined few-body systems, magnetic properties of cold fermionic atoms in optical lattices, and vortex formation in few-body systems. The dissertation also studies the properties of the SDFT-LSDA method for many-body calculations itself. The dissertation comprises five original papers, which are presented following an introduction to the fields of research, and the methods used, and the systems studied. Paper I investigates symmetry-breaking states in quantum dots, and the reliability of SDFT-LSDA for such systems. It is found that SDFT-LSDA may introduce artificial energy splittings between the members of a degenerate spin multiplet in the ground state. Paper II investigates the reliability of SDFT-LSDA when used to calculate gaps, and addition and removal energies in few-body systems. It is found that, contrary to studies of atoms and bilk solids, Kohn-Sham eigenvalues can be used to calculate addition and removal energies in parabolically confined systems. Also, in Paper II, van der Waals blockade is predicted to occur in systems of cold atoms, in analogy to Coulomb blockade in electronic systems. In Papers III and IV, mean-field theory is used to study the magnetic properties of cold fermionic atoms in an optical lattice. The results are compared with a similar study for quantum-dot lattices. It is found that there is a rich magnetic phase diagram, with non-magnetic, ferromagnetic, and anti-ferromagnetic states. The phase diagram of the optical lattice is found to be very similar to the phase diagram of the quantum-dot lattice. Paper V uses exact diagonalization to study vortex formation in rotating few-body quantum systems. Systems consisting of Coulomb-interacting fermions (electrons), Coulomb-interacting bosons, and bosons with a short-range interaction are studied. It is found that vortex formation in these systems has universal properties.