01292nas a2200145   4500008004100000245004900041210004900090300001200139490000700151520086800158100002901026700002101055700002401076856004601100       2019                        eng d00aGround state energy of mixture of Bose gases0 aGround state energy of mixture of Bose gases  a19500050 v313 a<p>We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N−1), we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.</p>1 aMichelangeli, Alessandro1 aNam, Phan, Thanh1 aOlgiati, Alessandro  uhttps://doi.org/10.1142/S0129055X1950005301947nas a2200145   4500008004100000245007100041210006800112260002100180300001200201490000700213520147800220100002901698700002401727856005001751       2017                        eng d00aGross-Pitaevskii non-linear dynamics for pseudo-spinor condensates0 aGrossPitaevskii nonlinear dynamics for pseudospinor condensates  bTaylor & Francis  a426-4640 v243 a<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 Schrödinger 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 Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’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>1 aMichelangeli, Alessandro1 aOlgiati, Alessandro  uhttps://doi.org/10.1080/14029251.2017.1346348