A remark on the mean-field dynamics of many-body bosonic systems with random interactions

TL;DR

This paper rigorously establishes that the mean-field limit for bosonic systems with random, bounded interactions can be described by a nonlinear Hartree equation, extending Egorov's theorem to such stochastic many-body quantum systems.

Contribution

It provides a rigorous proof that the many-body quantum dynamics with random interactions converges to a nonlinear mean-field evolution described by the Hartree equation.

Findings

Mean-field limit holds for almost-surely bounded random interactions.

Many-body quantum evolution approximates a nonlinear Hartree equation.

Extension of Egorov's theorem to systems with randomness.

Abstract

The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a single particle nonlinear evolution that is described by the Hartree equation. This is an Egorov-type theorem for many-body quantum systems with random interactions.