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We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in $R^3$. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdos, Schlein and Yau, cite{esy1,esy2,esy3,esy4}.
We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ${mathbb R}^3$. Moreover, we show that an energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific
In arXiv:1201.4067 and arXiv:1611.08030, Eyink and Shi and Chibbaro et al., respectively, formally derived an infinite, coupled hierarchy of equations for the spectral correlation functions of a system of weakly interacting nonlinear dispersive waves
We study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimen
We study the time-evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. Under a physically motivated assumption on the energy of the initial data, we show that condensation is preserved by the many-body evolution an
We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order $N^{-1+kappa}$, for $kappa>0$. Assuming that $kappain (0;1/43)$, we show that low-energy states of the system exhibit complete