A Central Limit Theorem in Many-Body Quantum Dynamics

2011/11/29 by Gérard Ben Arous, Kay Kirkpatrick, Arous, Gerard Ben +3
Computer Science · Physics and Astronomy · #60F05 #81U05 #81U30 #81V70 #82C10 #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.1111.6999

openalex publication_date 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system.

Citations

• A quantum-mechanical central limit theorem

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