Weak Edgeworth expansion for the mean-field interacting Bose gas

Abstract

We consider the ground state and the low-energy excited states of a system of $N$ identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive an Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in $1/\sqrt{N}$ . For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher order corrections are given by an Edgeworth-type expansion.

arXiv comment31 pages. v3: this version is to appear in Letters in Mathematical Physics

References in corpus (10)

• A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Beyond Bogoliubov Dynamics
• Multivariate Central Limit Theorem in Quantum Dynamics
• Edgeworth expansions for weakly dependent random variables
• Central Limit Theorem for Bose-Einstein Condensates
• Central limit theorem for Bose gases interacting through singular potentials
• A large deviation principle in many-body quantum dynamics
• Large deviation estimates for weakly interacting bosons
• A note on dependent random variables in quantum dynamics

Cited by in corpus (3)

• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications
• A Note on the Binding Energy for Bosons in the Mean-field Limit