Dynamics of Large Boson Systems with Attractive Interaction and a Derivation of the Cubic Focusing NLS in ${\mathbb{R}}^3$

Jacky Jia Wei Chong

We consider a system of $N$ bosons where the particles experience a short range two-body interaction given by $N^{-1}{v}_N(x)=N^{3\beta -1}v(N^{\beta }x)$ where $v\in C_c^{\infty }({\mathbb{R}}^3)$,…