Michelangeli, AlessandroOlgiati, Alessandro2018-03-232018-03-232018-03https://openscience.sissa.it/handle/1963/35311We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the manybody Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.eneffective non-linear evolution equationsmany-body quantum dynamicsspinor Bose-Einstein condensatespartial tracereduced density matrixmean-field and Gross-Pitaevskii scalingcubic NLScoupled non-linear Schrödinger system.Preprint