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# Advances in Theoretical and Mathematical Physics

## Volume 21 (2017)

### Number 3

### Bogoliubov correction to the mean-field dynamics of interacting bosons

Pages: 683 – 738

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n3.a4

#### Authors

#### Abstract

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

We gratefully acknowledge the financial supports by the REA grant agreement No. 291734 (PTN), as well as the support of the National Science Center (NCN) grant No. 2012/07/N/ST1/03185 and the Austrian Science Fund (FWF) project Nr. P 27533-N27 (MN).