Norm approximation for many-body quantum dynamics and Bogoliubov theory

We review some recent results on the norm approximation to the Schrödinger dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3β-1}w(N^β(x-y))$ with $0\le β<1/2$, and show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation.

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