Exact bound states and spin segregation for noninteracting trapped fermions in a spin-dependent harmonic trapping potential

Abstract

We investigate the spectral properties of coupled noninteracting trapped fermions in a spin-dependent harmonic trapping potential. It is shown that for certain specific parameter conditions, there exist an infinite number of the exact energies and wave functions of the bound states. Two different types of the exact energies have been identified, and they are associated with the level-crossings and avoided level-crossings, respectively. In addition, the effect of the energy bias on the energy spectrum is also discussed. In particular, it is found that under suitably chosen parameter conditions, the exact wave functions of the bound states provide an analytical demonstration of the existence of the spin segregation.