Abstract (EN)

We consider a 2D quantum system of N bosons in a trapping potential |x|s, interacting via a pair potential of the form N2β−1w(Nβx). 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.