%0 Journal Article
%T Bogoliubov correction to the mean-field dynamics of interacting bosons
%A Phan Th¨¤nh Nam
%A Marcin Napi¨®rkowski
%J Mathematics
%D 2015
%I arXiv
%X We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3\beta-1} w(N^\beta(x-y))$. For fixed $0\leq \beta <1/3$ and large $N$, we obtain a norm approximation to the many-body evolution in the $N$-particle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory.
%U http://arxiv.org/abs/1509.04631v2