Bogatskiy A, Wiegmann P
Kadanoff Center for Theoretical Physics, University of Chicago, 5620 South Ellis Ave, Chicago, Illinois 60637, USA.
Phys Rev Lett. 2019 May 31;122(21):214505. doi: 10.1103/PhysRevLett.122.214505.
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 are 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.
我们证明，涡旋物质，即在不可压缩二维流（如快速旋转的超流体或具有类符号涡旋的湍流）中密集排列的涡旋，呈现出（i）一个涡度边界层（涡度层）和（ii）一个局限于涡度层内的非线性波，即边缘波。这两者均完全是涡旋拓扑性质的效应。如果将涡旋物质近似为连续的涡度斑块，那么这两者都会消失。边缘波由可积的本杰明 - 戴维斯 - 奥诺方程 governing ，呈现出具有量子化总涡度的孤子。量子化孤子通过其动力学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所致。我们还将该动力学与圆的微分同胚的维拉索罗 - 博特群的作用联系起来，其中奇粘性参数化了中心扩张。我们的边缘波是分数量子霍尔效应边缘态的流体动力学类似物。
