Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems
Mathematical Physics
2015-06-26 v3 math.MP
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 Schr\"odinger equation in a suitable scaling limit. The result is extended to -particle density matrices for all positive integer .
Keywords
Cite
@article{arxiv.math-ph/0508010,
title = {Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems},
author = {Laszlo Erdos and Benjamin Schlein and Horng-Tzer Yau},
journal= {arXiv preprint arXiv:math-ph/0508010},
year = {2015}
}
Comments
72 pages, 17 figures. Final version