囚禁有限unitary费米气体的压强与状态方程

目的研究非对称与球对称简谐势阱中有限unitary费米气体的压强与状态方程。方法运用分数不相容统计法。结果求出了非对称与球对称简谐势阱中有限unitary费米气体的压强张量以及压强与内能的关系,导出了球对称势阱中的状态方程并给出了低温强简并近似和高温弱简并近似。结论揭示了有限unitary费米气体系统压强的有限尺度效应,给出了有限尺度效应判据。指出了球对称简谐势阱中有限unitary费米气体的压强在空间3个方向上各向同性与非对称势阱中压强张量在空间3个方向各向异性的特征,阐明了非对称势阱中沿着势阱圆频率低的方向压强张量高,沿着势阱圆频率高的方向压强张量低的规律,揭示了压强张量在空间3个方向各向异性的物理本质。

The pressure and equation of state for a trapped finite unitary Fermi gas

Purposes—To study the pressure and the equations of state for finite unitary Fermi gas in three-dimensional spherically symmetric harmonic trap and asymmetric harmonic trap.Methods—Fractional exclusion statistics based on the accurate density of states for a finite system in a harmonic trap are used to achieved the aforesaid purposes.Results—The pressure tensor and the relationship be-tween pressure and internal energy of a finite unitary Fermi gas are derived.The equations of state for a finite unitary Fermi gas in three-dimensional spherically symmetric harmonic trap are gained,and the low-temperature strong degenerate approximation and the high-temperature weakly degenerate ap-proximation for the equation of state are given.Conclusions—The finite-size effect of the pressure for finite unitary Fermi gas is revealed and the criteria of finite-size effect are given.The pressure tensor is isotropic in a spherically symmetric harmonic trap w hile it is anisotropic in an asymmetric harmonic trap,and the pressure tensor is high in the asymmetric harmonic trap along the direction of the small frequency w hile the pressure tensor is low along the direction of the high frequency of the harmonic trap.The physical essence of pressure tensor anisotropy is revealed.