A note on the validity of Bogoliubov correction to mean-field dynamics

@article{Nam2016ANO,
  title={A note on the validity of Bogoliubov correction to mean-field dynamics},
  author={P. T. Nam and M. Napi{\'o}rkowski},
  journal={arXiv: Mathematical Physics},
  year={2016}
}
We study the norm approximation to the Schr\"odinger dynamics of $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3\beta-1}w(N^{\beta}(x-y))$. 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 $0\le \beta<1/2$. The range of $\beta$ is expected to be… Expand
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