On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics (Q2436319)

In this paper, by proving the limit of a BBGKY hierarchy whose limit is not even formally known since it contains \((\infty -\infty)\), the authors have rigorously derived the 2D cubic nonlinear Schrödinger equation from a 3D quantum many-body dynamic and they have accurately described the 3D to 2D phenomenon by establishing the exact emergence of the coupling constant \((\int|h_1(z)|^4dz)\). This is the first direct rigorous treatment of the 3D to 2D dynamic problem in the literature.