Local enhancement of the mean-field approximation for bosons

TL;DR

This paper introduces a local enhancement of the mean-field approximation for Bose-Einstein condensates on a lattice, providing bounds on the approximation error at positive distances from the initial state using new propagation bounds.

Contribution

It develops a novel local error bound for the mean-field approximation in BECs and introduces a variant of the ASTLO method for fluctuation analysis.

Findings

Error bounds improve with distance from initial condensate

Ballistic propagation bounds on fluctuations established

New ASTLO variant developed for fluctuation dynamics

Abstract

We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance $\rho>0$ from the initial BEC, the mean-field approximation error at time $t\leq \rho/v$ is bounded as $\rho^{-n}$, for arbitrarily large $n\geq 1$. This is a consequence of new ballistic propagation bounds on the fluctuations around the condensate. To prove this, we develop a variant of the ASTLO (adiabatic spacetime localization observable) method for the particle non-conserving generator of the fluctuation dynamics around Hartree states.