@article {doi:10.1080/14029251.2017.1346348,
	title = {Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates},
	journal = {Journal of Nonlinear Mathematical Physics},
	volume = {24},
	number = {3},
	year = {2017},
	pages = {426-464},
	publisher = {Taylor \& Francis},
	abstract = {<p>We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr{\"o}dinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schr{\"o}dinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl{\textquoteright}s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.</p>},
	doi = {10.1080/14029251.2017.1346348},
	url = {https://doi.org/10.1080/14029251.2017.1346348},
	author = {Alessandro Michelangeli and Alessandro Olgiati}
}
