论文标题
平均场相互作用的弱Edgeworth扩展
Weak Edgeworth expansion for the mean-field interacting Bose gas
论文作者
论文摘要
我们考虑了$ n $相同玻色子系统的基态和低能激发状态，并在平均场缩放机制中进行相互作用。对于基态，我们为有限的单体操作员的波动得出了Edgeworth的扩展，该扩展将校正为中心限制定理，以$ 1/\ sqrt {n} $中的任何顺序定理。对于合适的激发态，我们表明限制分布是多项式时间的正态分布，并且高阶校正由Edgeworth型扩展给出。
We consider the ground state and the low-energy excited states of a system of $N$ identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive an Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in $1/\sqrt{N}$ . For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher order corrections are given by an Edgeworth-type expansion.
