01371nas a2200145   4500008004100000245008000041210007100121260002400192300001100216490000700227520088900234100002901123700002401152856004901176       2018                        eng d00aEffective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate0 aEffective nonlinear spinor dynamics in a spin1 Bose–Einstein con  bIOP Publishingcsep  a4052010 v513 a<p>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.</p>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 a<p>We 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.</p>1 aOlgiati, Alessandro1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto  uhttps://doi.org/10.1007/978-3-319-58904-6_14