A Central Limit Theorem in Many-Body Quantum Dynamics

Gérard Ben Arous, Kay Kirkpatrick, Benjamin Schlein

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Pages (from-to)371-417
Number of pages47
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Jul 1 2013


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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