Entropy Chaos and Bose-Einstein Condensation

TL;DR

This paper rigorously proves the entropy-chaos property for a system of interacting Bose particles, showing convergence of the one-particle diffusion to a measure linked to the Gross-Pitaevskii ground state.

Contribution

It establishes the entropy-chaos property for Bose systems in the Gross-Pitaevskii limit, connecting microscopic dynamics with the mean-field ground state.

Findings

Weak convergence of one-particle measures to the Gross-Pitaevskii minimizer

Rigorous proof of entropy-chaos in Bose systems

Connection between microscopic diffusions and mean-field theory

Abstract

We prove the entropy-chaos property for the system of N undistinguishable interacting diffusions rigorously associated with the ground state of N trapped Bose particles in the Gross-Pitaevskii scaling limit of infinite particles. On the path-space we show that the sequence of probability measures of the one-particle interacting diffusion weakly converges to a limit probability measure, uniquely associated with the minimizer of the Gross-Pitaevskii functional.