(color online) Contour plots of time evolutions of the density distribution (a) and the momentum distribution (b) for a trapped system with 50 fermions, L = 600, , and . (c) The contour plot of the long time evolution of the density distribution for the same trapped system shown in panel (a). (d) The group velocity versus the local density for trapped fermionic systems with . Inset in panel (d): the group velocity versus the phase difference for trapped fermionic systems with 50 fermions, L = 600, and .