@article{632,
abstract = {We consider a 2D quantum system of N bosons in a trapping potential |x|s, interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all 0 < β < (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 Schrödinger energy functional. Our result covers the focusing case (w < 0) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X. Chen and J. Holmer for harmonic traps (s = 2). Together with the BBGKY hierarchy approach used by these authors, our result implies the convergence of the many-body quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < β < 3/4. },
author = {Lewin, Mathieu and Nam, Phan and Rougerie, Nicolas},
journal = {Proceedings of the American Mathematical Society},
number = {6},
pages = {2441 -- 2454},
publisher = {American Mathematical Society},
title = {{A note on 2D focusing many boson systems}},
doi = {10.1090/proc/13468},
volume = {145},
year = {2017},
}