A Central Limit Theorem in Many-Body Quantum Dynamics
Mathematical Physics
2012-03-27 v3 math.MP
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.
Cite
@article{arxiv.1111.6999,
title = {A Central Limit Theorem in Many-Body Quantum Dynamics},
author = {Gerard Ben Arous and Kay Kirkpatrick and Benjamin Schlein},
journal= {arXiv preprint arXiv:1111.6999},
year = {2012}
}
Comments
42 pages; some references added