A Central Limit Theorem in Many-Body Quantum Dynamics

Details A Central Limit Theorem in Many-Body Quantum Dynamics A Central Limit Theorem in Many-Body Quantum Dynamics

2011-11-29

arxiv.org/abs/1111.6999v3

Physics

Mathematical Physics

42 pages; some references added

Scientific paper

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.

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