Mean field limit for many-particle interactions

TL;DR

This paper establishes a rigorous 1/N error bound for approximating the dynamics of N bosons with a generalized nonlinear Hartree equation, extending previous results to many-particle bounded potentials.

Contribution

It generalizes existing error bounds to include permutation symmetric bounded many-particle interactions in the mean field limit.

Findings

Error scales as 1/N for all times

Valid for permutation symmetric bounded potentials

Extends previous 2-particle potential results

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