Asymptotic expansion of the mean-field approximation
Quantum Physics
2017-10-11 v1 Mathematical Physics
Analysis of PDEs
Dynamical Systems
math.MP
Abstract
We established and estimate the full asymptotic expansion in integer powers of 1 N of the [ \sqrt N ] first marginals of N-body evolutions lying in a general paradigm containing Kac models and non-relativistic quantum evolution. We prove that the coefficients of the expansion are, at any time, explicitly computable given the knowledge of the linearization on the one-body meanfield kinetic limit equation. Instead of working directly with the corresponding BBGKY-type hierarchy, we follows a method developed in [22] for the meanfield limit, dealing with error terms analogue to the v-functions used in previous works. As a by-product we get that the rate of convergence to the meanfield limit in 1 N is optimal.
Cite
@article{arxiv.1710.03618,
title = {Asymptotic expansion of the mean-field approximation},
author = {Thierry Paul and Mario Pulvirenti},
journal= {arXiv preprint arXiv:1710.03618},
year = {2017}
}