Expansion of a free Fermi gas released from an isotropic trapping potential

We consider a system of non-interacting fermions prepared in the many-body ground state of an isotropic trapping potential in any dimension, and investigate the ballistic expansion of the fermionic cloud after the potential is suddenly released. Using semi-classical techniques, we derive the full late-time profile of the expanding cloud in the regime when the fermion number is large. We thus obtain explicit expressions for power-law potentials with arbitrary exponent $a$ and in all dimensions $d$. The momentum distribution and the spatial profile of the cloud exhibit a universal edge exponent $d/a$, thus generalizing the Wigner semi-circle law and the Thomas-Fermi distribution.