Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
We derive rigorously, for both ${\Bbb R}^2$ and $[{-}L,L]^{\times 2}$, the cubic nonlinear Schr\"odinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution …