%0 Journal Article %J Analysis and Mathematical Physics %D 2017 %T Mean-field quantum dynamics for a mixture of Bose–Einstein condensates %A Alessandro Michelangeli %A Alessandro Olgiati %X

We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schrödinger dynamics is effectively described by a system of coupled cubic non-linear Schrödinger equations, one for each component.

%B Analysis and Mathematical Physics %V 7 %P 377–416 %8 Dec %G eng %U https://doi.org/10.1007/s13324-016-0147-3 %R 10.1007/s13324-016-0147-3 %0 Report %D 2016 %T Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type %A Alessandro Michelangeli %A Andrea Ottolini %X We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan- Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Kreĭn, Višiik, and Birman. We identify the explicit `Kreĭn-Višik-Birman extension param- eter' as an operator on the `space of charges' for this model (the `Kreĭn space') and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we re- produce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach. %G en %U http://urania.sissa.it/xmlui/handle/1963/35267 %1 35573 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:25:08Z No. of bitstreams: 1 SISSA_preprint_65-2016-MATE.pdf: 252490 bytes, checksum: 59617b8bff76543e4ea137b885bf1254 (MD5)