Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics

TL;DR

This paper provides quantitative estimates on how quickly the microscopic quantum evolution of N-boson systems approaches the mean field Hartree dynamics as N becomes large.

Contribution

It offers new bounds on the rate of convergence of N-body quantum dynamics to the Hartree mean field limit, enhancing understanding of quantum fluctuations.

Findings

Established bounds on the difference between quantum and mean field states.

Quantified the rate at which quantum dynamics converge to the Hartree equation.

Improved previous estimates on convergence speed.

Abstract

The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schroedinger equation and the orthogonal projection onto the solution of the Hartree equation.