Norm approximation for many-body quantum dynamics and Bogoliubov theory

Abstract

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 $N^{3\beta -1}w(N^{\beta }(x-y))$ with $0\le \beta <1/2$, and show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation.

A contribution for the volume "Advances in Quantum Mechanics: contemporary trends and open problems" of the INdAM-Springer series