Charge and spin dynamics of interacting Fermions in a one dimensional harmonic trap

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We study an atomic Fermi gas interacting through repulsive contact forces in a one dimensional harmonic trap. Bethe-Ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation the edges cause a giant increase of the separation between these modes.