The Hartree-von Neumann limit of many body dynamics

TL;DR

This paper proves that in the mean-field regime, the complex many-body von Neumann dynamics with bounded interactions converges to the simpler Hartree-von Neumann dynamics, providing explicit bounds for this convergence.

Contribution

It establishes the convergence of many-body von Neumann dynamics to Hartree-von Neumann dynamics with explicit bounds in the mean-field regime.

Findings

Proves convergence with explicit bounds

Validates the mean-field approximation for bounded interactions

Bridges many-body quantum dynamics with effective single-particle equations

Abstract

In the mean-field regime, we prove convergence (with explicit bounds) of the many-body von Neumann dynamics with bounded interactions to the Hartree-von Neumann dynamics.