A note on the validity of Bogoliubov correction to mean-field dynamics
arXiv:1604.05240
Abstract
We study the norm approximation to the Schrödinger dynamics of $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3β-1}w(N^β(x-y))$. Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all $0\le β<1/2$. The range of $β$ is expected to be optimal for this large class of initial states.
Final version, to appear in Journal de Mathématiques Pures et Appliquées