Derivation of the Cubic Non-linear Schr'odinger Equation from Quantum Dynamics of Many-Body Systems

摘要

We prove rigorously that the one-particle density matrix of three dimensionalinteracting Bose systems with a short-scale repulsive pair interactionconverges to the solution of the cubic non-linear Schr\"odinger equation in asuitable scaling limit. The result is extended to $k$-particle density matricesfor all positive integer $k$.