Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data

TL;DR

This paper provides estimates on how quickly the many-body Schrödinger dynamics converges to the nonlinear Hartree equation for Boson systems with factorized initial data, considering specific interaction potentials.

Contribution

It offers new quantitative convergence rate estimates for the mean field limit of Boson systems with two-body interactions.

Findings

Derived explicit 1/N convergence rates

Applicable to potentials in L^3 + L^∞ spaces

Enhances understanding of mean field approximation accuracy

Abstract

The mean field dynamics of an $N$-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schr\"{o}dinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data with two-body interaction potential $V$ in $L^3 (\mathbb{R}^3)+ L^{\infty} (\mathbb{R}^3)$.