Interacting fermions in a two-dimensional trap and fractional exclusion statistics

We consider N fermions in a two-dimensional harmonic oscillator potential i nteracting with a very short-range repulsive pair-wise potential. The groun d-state energy of this system is obtained by performing a Thomas-Fermi as w ell as a self-consistent Hartree-Fock calculation. The two results are show n to agree even for a small number of particles. We next use the finite-tem perature Thomas-Fermi method to demonstrate that in the local density appro ximation, these interacting fermions are equivalent to a system of noninter acting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto a system of N noninteracting quasiparticle s enables us to predict the energies of the ground and excited states of th e N-body system.