We 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 many-body 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.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttps://doi.org/10.1088%2F1751-8121%2Faadbc201139nas a2200157 4500008004100000020002200041245007400063210006900137260004400206300001400250520058600264100002400850700002900874700002900903856004900932 2017 eng d a978-3-319-58904-600aEffective Non-linear Dynamics of Binary Condensates and Open Problems0 aEffective Nonlinear Dynamics of Binary Condensates and Open Prob aChambSpringer International Publishing a239–2563 aWe report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

1 aOlgiati, Alessandro1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_14