Diffusion Monte Carlo Calculations for Trapped Fermi Gases

Monte Carlo methods are particularly useful to test the validity of the effective theories. Blume and Greene have used diffusion Monte Carlo to study the corrections to the Gross-Pitaevskii equation for bosons [1]. We study the ground state energy of a trapped degenerate Fermi gas using Monte Carlo methods. We compare mean field results and higher order corrections with our calculations. As in the case of bosons, effective theories predict a collapse of a Fermi gas at negative $a_{0}$ [2]. We analyze the possibility of collapse considering finite range interactions. [1] D. Blume and Chris H. Greene, Phys. Rev. A 63, 063601 (2001). [2] S. T. Rittenhouse et al, arXiv:cond-mat/0510454.