# A note on 2D focusing many-boson systems

@article{Lewin2015ANO,
title={A note on 2D focusing many-boson systems},
author={Mathieu Lewin and Phan Th{\`a}nh Nam and Nicolas Rougerie},
journal={arXiv: Mathematical Physics},
year={2015}
}
• Published 30 September 2015
• Physics, Mathematics
• arXiv: Mathematical Physics
We consider a 2D quantum system of $N$ bosons in a trapping potential $|x|^s$, interacting via a pair potential of the form $N^{2\beta-1} w(N^\beta x)$. We show that for all $0 \textless{} \beta \textless{} (s+1)/(s+2)$, the leading order behavior of ground states of the many-body system is described in the large $N$ limit by the corresponding cubic nonlinear Schr{o}dinger energy functional. Our result covers the focusing case ($w \leq 0$) where even the stability of the many-body system is not…
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These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics. A general strategy for the justification of effective