We consider a system of N bosons in the limit $$N \rightarrow \infty $$ N → ∞ , 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 nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.

中文翻译：

---

玻色气体通过奇异势相互作用的中心极限定理

我们考虑在极限 $$N \rightarrow \infty $$ N → ∞ 中的 N 个玻色子系统，通过奇异势相互作用。对于显示玻色-爱因斯坦凝聚的初始数据，多体时间演化可以通过凝聚波函数的三次非线性薛定谔方程周围的二次波动动力学很好地近似。我们表明这些波动满足（多变量）中心极限定理。