On the mean field approximation of many-boson dynamics

TL;DR

This paper proves the validity of the mean-field approximation for quantum many-boson systems under broad conditions, using advanced mathematical tools to unify and enhance existing results.

Contribution

It provides a unified and improved proof of the mean-field approximation's correctness for many-boson dynamics, employing quantization, phase-space analysis, and measure transportation.

Findings

Mean-field approximation is valid under general assumptions.

The proof unifies and improves previous results.

Uses advanced mathematical techniques for the proof.

Abstract

We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in infinite dimensional spaces, phase-space analysis and measure transportation techniques.