In this paper, we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Pad approximant. The virial expansion is a high-temperature and low-density expansion and in practice, often, only the first several virial coefficients can be obtained. For Bose gases, we determine the BEC phase transition from a truncated virial expansion. For Fermi gases, we recover the low-temperature and high-density result from the virial expansion.

中文翻译：

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量子气体奇异性质的近似方法：理想情况

在本文中，我们展示了如何通过 Pad 近似从高温低密度近似恢复理想量子气体的低温高密度信息。维里膨胀是一种高温低密度膨胀，在实践中，通常只能获得前几个维里系数。对于 Bose 气体，我们从截断的维里膨胀确定 BEC 相变。对于费米气体，我们从维里膨胀中恢复了低温和高密度的结果。