Edge Wave and Boundary Layer of Vortex Matter
Edge Wave and Boundary Layer of Vortex Matter
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DOI：
10.1103/physrevlett.122.214505
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发表时间：
2019-05-30
影响因子：
8.6
通讯作者：
Wiegmann, P.
中科院分区：
文献类型：
--
作者：
Bogatskiy, A.;Wiegmann, P.
我们表明，涡旋物质，即，在不可压缩的二维流，如快速旋转的超流体或湍流的符号涡的密集组装，表现出（i）涡的边界层（涡层）和（ii）非线性波内的涡层，边缘波。这两种现象都是旋涡的拓扑性质的结果。如果把涡旋物质近似为一个连续的涡量片，则这两种情况都消失了。边缘波由可积的Benjamin-Davis-Ono方程控制，表现出具有量子化总涡度的孤子。量子化孤子通过其动力学特性揭示了涡旋的拓扑性质。边缘波和涡度层是由于涡旋物质的奇粘性引起的。我们还确定的Virasoro-Bott组的圆，奇粘度parametrizes的中心扩展的graphomorphisms的行动的动力学。我们的边缘波是分数量子霍尔效应的边缘态的流体动力学模拟。
We show that vortex matter, that is, a dense assembly of vortices in an incompressible two-dimensional flow, such as a fast rotating superfluid or turbulent flows with signlike eddies, exhibits (i) a boundary layer of vorticity (vorticity layer) and (ii) a nonlinear wave localized within the vorticity layer, the edge wave. Both are solely an effect of the topological nature of vortices. Both arc lost if vortex matter is approximated as a continuous vorticity patch. The edge wave is governed by the integrable Benjamin-Davis-Ono equation, exhibiting solitons with a quantized total vorticity. Quantized solitons reveal the topological nature of the vortices through their dynamics. The edge wave and the vorticity layer are due to the odd viscosity of vortex matter. We also identify the dynamics with the action of the Virasoro-Bott group of diffeomorphisms of the circle, where odd viscosity parametrizes the central extension. Our edge wave is a hydrodynamic analog of the edge states of the fractional quantum Hall effect.