Effective Non-linear Dynamics of Binary Condensates and Open Problems
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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.
KeywordsCoupled nonlinear Schrödinger system Cubic NLS Effective non-linear evolution equations Gross-Pitaevskii scaling Manybody quantum dynamics Mean-field regime Mixture condensates Partial trace Reduced density matrix
Partially supported by the 2014–2017 MIUR-FIR grant “Cond-Math: Condensed Matter and Mathematical Physics”, code RBFR13WAET and by Gruppo Nazionale per la Fisica Matematica (GNFM-INdAM).
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