Central limit theorem for Bose gases interacting through singular potentials

Abstract

We consider a system of $N$ bosons in the limit $N\to \infty$, interacting through singular potentials. For initial data exhibiting Bose-Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic non-linear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.

arXiv comment26 pages

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Cited by in corpus (7)

• A large deviation principle in many-body quantum dynamics
• Large deviation estimates for weakly interacting bosons
• Weak Edgeworth expansion for the mean-field interacting Bose gas
• A note on dependent random variables in quantum dynamics
• Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications
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