Mean field limit for many-particle interactions
Quantum Physics
2020-06-11 v1 Mathematical Physics
math.MP
Abstract
We provide an error bound for approximating the time evolution of N bosons by a generalized nonlinear Hartree equation. The bosons are assumed to interact via permutation symmetric bounded many-particle potentials and the initial wave-function is a product state. We show that the error between the actual evolution of a single particle derived from tracing out the full N-particle Schrodinger equation and the solution to the mean field approximate generalized nonlinear Hartree equation scales as 1/N for all times. Our result is a generalization of rigorous error bounds previously given for the case of bounded 2-particle potentials
Cite
@article{arxiv.2006.05486,
title = {Mean field limit for many-particle interactions},
author = {Can Gokler},
journal= {arXiv preprint arXiv:2006.05486},
year = {2020}
}