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The spectrum of two spin-up and two spin-down fermions in a trap iscalculated using a correlated gaussian basis throughout the range of theBCS-BEC crossover. These accurate calculations provide a few-body solution tothe crossover problem. This solution is used to study the time-evolution of thesystem as the scattering length is changed, mimicking experiments with Fermigases near Fano-Feshbach resonances. The structure of avoiding crossings in thespectrum allow us to understand the dynamics of the system as a sequence ofLandau-Zener transitions. Finally, we propose a ramping scheme to studyatom-molecule coherence.Comment: 4 pages, final version to appear in PR

Spectrum and Dynamics of the BCS-BEC Crossover from a Few-Body Perspective