Bogoliubov correction to the mean-field dynamics of interacting bosons

Abstract

We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3β-1} w(N^β(x-y))$. For fixed $0\leq β<1/3$ 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.

Final version, to appear in ATMP