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.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 239–256 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_14 %R 10.1007/978-3-319-58904-6_14 %0 Journal Article %J J. Phys. A 43 (2010) 474014 %D 2010 %T Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs %A Gianfausto Dell'Antonio %A Emanuele Costa %X We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph. %B J. Phys. A 43 (2010) 474014 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4106 %1 298 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:09:12Z\\nNo. of bitstreams: 1\\n1004.4750v2.pdf: 273649 bytes, checksum: ff34b6647ba206615715d6c764115064 (MD5) %R 10.1088/1751-8113/43/47/474014