In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of $N$ $d$-dimensional bosons for large $N$. The bosons initially form a Bose-Einstein condensate and interact with each other via a pair potential of the form $(N-1)^{ -1}N^{ d\beta}v(N^\beta\cdot)$ for $\beta\in[0,\frac{ 1}{ 4d})$. We derive a sequence of $N$-body functions which approximate the true many-body dynamics in $L^2(\mathbb{ R}^{ d N})$-norm to arbitrary precision in powers of $N^{ -1}$. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.
Categories: math-ph math.MP