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費米氣體

气体共振图谱

物理学中,費米氣體(Fermi gas),又稱為自由电子氣體(free electron gas)、费米原子气体,是一个量子统计力学中的理想模型,指的是一群不相互作用的費米子

費米氣體是理想氣體量子力學版本。在金屬內的電子、在半導體內的電子或在中子星裏的中子,都可以被視為近似於費米氣體。處於熱力平衡的費米氣體裏,費米子的能量分布,是由它們的數目密度(number density)、溫度、與尚存在能量量子態集合,依照費米-狄拉克統計的方程式而表徵。泡利不相容原理闡明,不允許兩個或兩個以上的費米子佔用同一个量子態。因此,在絕對零度,費米氣體的總能量大於費米子數量與單獨粒子基態能量的乘積,並且,費米氣體的壓力,稱為「簡併壓力」,不等於零。這與經典理想氣體的現象有很明顯的不同。簡併壓力使得中子星或白矮星能夠抵抗萬有引力的壓縮,因而得到穩定平衡,不致向內爆塌。

在低温下,玻色原子气体可以形成玻色-爱因斯坦凝聚(Bose-Einstein condensation, BEC),这是由爱因斯坦在1925年的理论而预言的。费米子由于泡利不相容原理,不能形成BEC。但可通过Feshbach共振,利用磁场调节费米原子间的相互作用,使费米子配对转变成玻色型粒子而形成BEC。

由於前述定義忽略了粒子與粒子之間的相互作用,費米氣體問題約化為研究一群獨立的費米子的物理行為的問題。這問題本身相當容易解析。一些更深奧,更進階,更精密的理論,牽涉到粒子與粒子之間的互相作用的理論(像費米液體理論或相互作用的微擾理論),時常會以費米氣體問題為研究的開端。

參考資料

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  • (美)沈星揚. 超流体. 北京:科学出版社. 1982. 

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費米氣體
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