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We consider spin-polarized mixtures of cold fermionic atoms on the BEC sideof the Feshbach resonance. We demonstrate that a strongly anisotropic confiningpotential can give rise to a double-peak structure in the axial distribution ofthe density difference and a polarization-dependent aspect ratio of theminority species. Both phenomena appear as a result of the breakdown of thelocal density approximation for the phase-separated regime. We speculate on theimplications of our findings for the unitary regime.Comment: Final published versio

Breakdown of the local density approximation in interacting systems of cold fermions in strongly anisotropic traps