Effective equations for quantum dynamics

TL;DR

This paper derives effective nonlinear equations from many-body quantum dynamics, providing rigorous bounds and a central limit theorem for fluctuations, advancing understanding of quantum mean field limits.

Contribution

It offers the first rigorous derivation of nonlinear Hartree equations with convergence rates and introduces a central limit theorem for fluctuations around these dynamics.

Findings

Rigorous derivation of nonlinear Hartree equations.

Quantitative bounds on convergence rates.

Central limit theorem for fluctuations.

Abstract

We report on recent results concerning the derivation of effective evolution equations starting from many body quantum dynamics. In particular, we obtain rigorous derivations of nonlinear Hartree equations in the bosonic mean field limit, with precise bounds on the rate of convergence. Moreover, we present a central limit theorem for the fluctuations around the Hartree dynamics.