我们能在BEC实验中区分巨正则和正则包围体吗？
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，多体系统的巨正则和正则描述所得到的结果没有明显的差异。在本文中，我们测试了这种说法的有效性有限系统作为一个例子，一个合奏的玻色子被困在一个一维谐波势阱。我们找到了正则配分函数的解析公式，并表明，对于100个被囚禁的原子，在玻色-爱因斯坦阈值附近，凝聚分数的巨正则和正则预测之间的差异达到10%。这种差异只随着原子数的增加而几何地减小。此外，我们调查数值的情况下，一个3D的“雪茄形状”的陷阱在相应的参数范围内，目前的BEC实验。
英文摘要：
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.
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。
