玻色-爱因斯坦凝聚体的涨落
Fluctuations of the Bose-Einstein condensate
摘要：
本文在正则系综支配下，对任意势场中无相互作用玻色子系统的玻色-爱因斯坦凝聚态的涨落进行了严格的分析。作为分析的结果，我们能够告诉的顺序的波动的凝析分数，以及其限制分布后，适当的中心和缩放。这产生了有趣的结果。例如，对于在转变温度附近的三维谐振阱中的$n$玻色子系统，凝聚分数的波动阶数为$n^{-1/2}$，极限分布是正态的，而对于三维均匀玻色气体，波动阶数为$n^{-1/3}$，极限分布是显式的非正态分布。对于2D谐波阱，涨落的阶数为$n^{-1/2}(\log n)^{1/2}$，其大于$n^{-1/2}$，但极限分布仍然是正态的。所有这些结果都是一般定理的简单推论。
英文摘要：
This article gives a rigorous analysis of the fluctuations of the Bose-Einstein condensate for a system of non-interacting bosons in an arbitrary potential, assuming that the system is governed by the canonical ensemble. As a result of the analysis, we are able to tell the order of fluctuations of the condensate fraction as well as its limiting distribution upon proper centering and scaling. This yields interesting results. For example, for a system of $n$ bosons in a 3D harmonic trap near the transition temperature, the order of fluctuations of the condensate fraction is $n^{-1/2}$ and the limiting distribution is normal, whereas for the 3D uniform Bose gas, the order of fluctuations is $n^{-1/3}$ and the limiting distribution is an explicit non-normal distribution. For a 2D harmonic trap, the order of fluctuations is $n^{-1/2}(\log n)^{1/2}$, which is larger than $n^{-1/2}$ but the limiting distribution is still normal. All of these results come as easy consequences of a general theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
