Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
arXiv:math-ph/0508010 · doi:10.1007/s00222-006-0022-1
Abstract
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to $k$-particle density matrices for all positive integer $k$.
72 pages, 17 figures. Final version