Semiclassical Analysis of Super-Shell Structure in Trapped Fermi Gases

Abstract: This dissertation investigates the oscillation part of the level density for trapped fermions. Analytical so-called trace formulae have been known for the two theoretically important potentials, the spherical cavity and harmonic oscillator, since more than thirty years. In this thesis we explore the regime in between those two limits, motivated by recent experiments with cold atomic Fermi gases. With semiclassical periodic orbit theory we analyze in particular the three-dimensional spherical system of a quartic perturbed harmonic oscillator. Super-shell structures are found and explained in terms of two classical periodic orbits, the diameter and the circle. This result is remarkable as the geometric degeneracies of those orbits are lower than those of the more common (star-like) type of orbits.