Exact results for the 1D interacting Fermi gas with arbitrary   polarization
  We investigate the 1D interacting two-component Fermi gas with arbitrary polarization. Exact results for the ground state energy, quasimomentum distribution functions, spin velocity and charge velocity reveal subtle polarization dependent quantum effects. 
M.T. Batchelor, M. Bortz, X.W. Guan and N. Oelkers