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We consider a one-dimensional optical lattice of three-dimensional HarmonicOscillators which are loaded with neutral fermionic atoms trapped into twohyperfine states. By means of a standard variational coherent-state procedure,we derive an effective Hamiltonian for this quantum model and the hamiltonianequations describing its evolution. To this end, we identify the algebra$\mathcal L$ of two-fermion operators --describing the relevant microscopicquantum processes of our model-- whereby the natural choice for the trial stateappears to be a so(2r) coherent state. The coherent-state parameters, playingthe role of dynamical variables for the effective Hamiltonian, are shown toidentify with the $\mathcal L$-operator expectation values thus providing aclear physical interpretation of this algebraic mean-field picture.Comment: 10 pages, 2 figures, submitted to J. Phys. B, Cortona BEC 2005  special issu

Mean-field algebraic approach to the dynamics of fermions in a 1D optical lattice