A note on dependent random variables in quantum dynamics

TL;DR

This paper studies the behavior of dependent random variables in quantum many-body dynamics, proving laws of large numbers and central limit theorems for certain operators in bosonic systems.

Contribution

It introduces a framework for analyzing dependent variables in quantum dynamics, establishing probabilistic limit theorems for bounded operators.

Findings

Bounded k-particle operators obey law of large numbers.

Central limit theorem holds for dependent quantum variables.

Results apply to weakly interacting bosons in mean field regime.

Abstract

We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both, a law of large numbers and a central limit theorem.