一维谐振势阱中玻色子的微正则系综与正则系综
Microcanonical versus canonical ensemble of bosons in a 1D harmonic trap
摘要：
我们考虑一个固定数目的非相互作用玻色子在一个谐波陷阱。精确确定微正则基态数涨落是一项困难的工作。有几个理论上的尝试来近似解决这个问题，特别是在1D模型中，使用数论中的一些渐近公式找到了解析结果。在这里，我们得到了精确的数量波动曲线，并表明这些精确的曲线是实质上不同于文献中的结果，小粒子数和有限的温度。此外，我们将展示如何使用正则热力学方法导出这些近似的微正则结果。
英文摘要：
We consider a fixed number of noninteracting bosons in a harmonic trap. The determination of the exact microcanonical ground state number fluctuation is a difficult enterprise. There have been several theoretical attempts to solve this problem approximately, especially in 1D models where analytic results were found using some asymptotic formulae from number theory. Here, we obtain the exact number fluctuation curves, and show that these exact curves are substantially different from the results presented in literature for small particle number and finite temperature. Further, we show how these approximate microcanonical results may be derived using a canonical thermodynamics approach.
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