A Central Limit Theorem in Many-Body Quantum Dynamics

Gerard Ben Arous, Kay Kirkpatrick, Benjamin Schlein

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)371-417
Number of pages47
JournalCommunications in Mathematical Physics
Volume321
Issue number2
DOIs
StatePublished - Jul 2013

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Quantum Dynamics
Central limit theorem
theorems
Hartree Equation
Mean-field Limit
Law of large numbers
Fock Space
Coherent States
Limiting Distribution
normal density functions
Gaussian distribution
Fluctuations
Form

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A Central Limit Theorem in Many-Body Quantum Dynamics. / Ben Arous, Gerard; Kirkpatrick, Kay; Schlein, Benjamin.

In: Communications in Mathematical Physics, Vol. 321, No. 2, 07.2013, p. 371-417.

Research output: Contribution to journalArticle

Ben Arous, Gerard ; Kirkpatrick, Kay ; Schlein, Benjamin. / A Central Limit Theorem in Many-Body Quantum Dynamics. In: Communications in Mathematical Physics. 2013 ; Vol. 321, No. 2. pp. 371-417.
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