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

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

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

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.

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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