Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 3

Bogoliubov correction to the mean-field dynamics of interacting bosons

Pages: 683 – 738



Phan Thành Nam (Institute of Science and Technology Austria, Klosterneuburg, Austria)

Marcin Napiórkowski (Institute of Science and Technology Austria, Klosterneuburg, Austria)


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.

Full Text (PDF format)

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).

Published 25 August 2017