# Strong Kac's chaos in the mean-field Bose-Einstein Condensation

## TL;DR

This paper introduces a stochastic approach to analyze the mean-field limit in Bose-Einstein Condensation, establishing convergence results for energy, path-space measures, and demonstrating strong Kac's chaos using probabilistic methods.

## Contribution

It provides a novel stochastic framework for mean-field limits in Bose-Einstein Condensation, proving strong Kac's chaos and related entropy and Fisher information chaos results.

## Key findings

- Convergence of ground state energy and components
- Strong Kac's chaos on path-space for particles
- Entropy and Fisher information chaos results

## Abstract

A stochastic approach to the (generic) mean-field limit in Bose-Einstein Condensation is described and the convergence of the ground state energy as well as of its components are established. For the one-particle process on the path space a total variation convergence result is proved. A strong form of Kac's chaos on path-space for the $k$-particles probability measures are derived from the previous energy convergence by purely probabilistic techniques notably using a simple chain-rule of the relative entropy. The Fisher's information chaos of the fixed-time marginal probability density under the generic mean-field scaling limit and the related entropy chaos result are also deduced.