@article {Michelangeli_2018,
	title = {Effective non-linear spinor dynamics in a spin-1 Bose{\textendash}Einstein condensate},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	volume = {51},
	number = {40},
	year = {2018},
	month = {sep},
	pages = {405201},
	publisher = {IOP Publishing},
	abstract = {<p>We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose{\textendash}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{\textendash}spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schr{\"o}dinger 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>},
	doi = {10.1088/1751-8121/aadbc2},
	url = {https://doi.org/10.1088\%2F1751-8121\%2Faadbc2},
	author = {Alessandro Michelangeli and Alessandro Olgiati}
}
@inbook {Olgiati2017,
	title = {Effective Non-linear Dynamics of Binary Condensates and Open Problems},
	booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems},
	year = {2017},
	pages = {239{\textendash}256},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {<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 Sch{\"o}dinger 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>},
	isbn = {978-3-319-58904-6},
	doi = {10.1007/978-3-319-58904-6_14},
	url = {https://doi.org/10.1007/978-3-319-58904-6_14},
	author = {Alessandro Olgiati},
	editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio}
}
@article {2008,
	title = {Equivalent definitions of asymptotic 100\% B.E.C.},
	journal = {Nuovo Cimento B 123 (2008) 181-192},
	number = {SISSA;102/2007/MP},
	year = {2008},
	abstract = {In the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.},
	doi = {10.1393/ncb/i2008-10521-y},
	url = {http://hdl.handle.net/1963/2546},
	author = {Alessandro Michelangeli}
}
