标题： 在BEC实验中，我们能区分巨正则系综和正则系综吗？ 显示英文标题

标题： Can We Distinguish Between the Grand Canonical and the Canonical Ensemble in a BEC Experiment?

摘要： 众所周知，在热力学极限下，通过巨正则和正则描述获得的多体系统的结果没有可观测的差异。 在本文中，我们使用一个被限制在1D谐波势阱中的玻色子系综作为例子，测试这一陈述在有限系统中的有效性。 我们得到了正则配分函数的解析公式，并表明对于100个被限制的原子，在玻色-爱因斯坦阈值附近，巨正则和正则预测的凝聚分数差异可达10%。 随着原子数的增加，这种差异仅以对数方式减少。 此外，我们数值研究了参数范围对应于当前BEC实验的3D“雪茄形”陷阱的情况。 显示英文摘要

摘要： It is well known that at the thermodynamic limit there are no observable differences in the results obtained by grand canonical and canonical descriptions of a many-body system. In the present paper, we test the validity of this statement for finite systems using as an example an ensemble of bosons trapped in a 1D harmonic potential well. We have found an analytical formula for the canonical partition function and shown that, for 100 trapped atoms, the discrepancy between the grand canonical and canonical predictions for the condensate fraction reaches 10% in the vicinity of the Bose-Einstein threshold. This discrepancy decreases only logarithmically as the number of atoms increases. Furthermore we investigate numerically the case of a 3D "cigar-shape" trap in the range of parameters corresponding to current BEC experiments.