LOW-LYING SUPERFLUID STATES IN A ROTATING ANNULUS.
LOW-LYING SUPERFLUID STATES IN A ROTATING ANNULUS.
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旋转环带中的低洼超流体状态。
DOI：
10.1103/physrev.153.285
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发表时间：
1967
期刊：
影响因子：
--
通讯作者：
A. Fetter
中科院分区：
文献类型：
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作者：
A. Fetter
用经典无粘流体模型研究了旋转液体He II在环形空间(R1<；r<；R2)中的低激发态。用图像法求出了具有环流κ的直线涡系和内筒周围环流Γ1相结合的系统的精确水动力解。计算了任意旋涡构型和L旋涡对称环的特殊构型的能量和角动量。如果将Γ1作为变分参数处理，则窄环内出现涡旋的临界角速度Ω0为(κπd2)ln(2 dπa)，其中d为环隙宽度，a为涡核半径。对于Ω<；Ω0，平衡态是一个无旋(无涡旋)流，具有量子化的循环nκ(n=1，2，⋯)；这些能级是等间距的，并且给定的量子态仅代表κ2πR2的窄角速度区间内的最低自由能，其中R是环空的平均半径。无旋环流的最大量子数为2πR2Ω0κ=2(Rd)2 ln(2 dπa)≫1.对于Ω>；Ω0，旋涡位于壁面中间的环状圆周上，并且随着Ω的增加，旋涡数量迅速增加.如果Γ1被约束为相同地消失，则在窄环隙中出现涡旋的临界角速度Ωc为κ2πRd量级，这相当于对于κ=hm的单量子化涡旋的Feynman临界速度vc=O(≪Md).在宽环隙的相反极限(R1和R2)中，平衡态与Vinen早期的计算一致.
The low-lying states of rotating liquid He II in an annulus (R 1< r< R 2) are studied with the model of a classical inviscid fluid. An exact hydrodynamic solution is obtained with the method of images for a system consisting of rectilinear vortices with circulation κ combined with circulation Γ 1 about the inner cylinder. The energy and angular momentum are calculated, both for an arbitrary configuration of vortices and for the particular configuration of a symmetric ring of l vortices. If Γ 1 is treated as a variational parameter, the critical angular velocity Ω 0 for the appearance of vortices in a narrow annulus is (κ π d 2) ln (2 d π a), where d is the width of the annulus and a is the radius of the vortex core. For Ω< Ω 0, the equilibrium state is an irrotational (vortex-free) flow with quantized circulation n κ (n= 1, 2,⋯); these levels are equally spaced, and a given quantum state represents the lowest free energy only in a narrow angular-velocity interval of κ 2 π R 2, where R is the mean radius of the annulus. The maximum quantum number of irrotational circulation is 2 π R 2 Ω 0 κ= 2 (R d) 2 ln (2 d π a)≫ 1. For Ω> Ω 0, the vortices lie on the circumference of a ring midway between the walls, and the number of vortices increases rapidly with Ω. If Γ 1 is constrained to vanish identically, the critical angular velocity Ω c for the appearance of vortices in a narrow annulus is of order κ 2 π Rd; this is equivalent to Feynman's critical velocity v c= O (ℏ md) for singly quantized vortices with κ= h m. In the opposite limit of a wide annulus (R 1≪ R 2), the equilibrium state is shown to agree with Vinen's earlier calculations.