One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates

We present a one-dimensional (1D) effective model for the evolution of a cigar-shaped Bose-Einstein condensate in time-dependent potentials whose radial component is harmonic. We apply this model to investigate the dynamics and expansion of condensates in 1D optical lattices, by comparing our predictions with recent experimental data and theoretical results. We also discuss negative-mass effects which could be probed during the expansion of a condensate moving in an optical lattice.