近日，南京大学的王新龙教授实验室取得一项新进展。经过不懈努力，他们发现类似于玻色-爱因斯坦凝聚态中集体激发法拉第水波的多边形图案。相关研究成果已于2023年12月7日在国际知名学术期刊《自然—物理学》上发表。

本文报道了在具有抛物面和其他凹底的振动水容器中观察到的多边形图案的法拉第波。这些图案以简单的几何对称图形形式出现，包括椭圆和七边形等，其波长远远大于毛细管长度，因此与先前研究的振动水滴或水洼的模式有着本质的不同，代表了凹盆地中非线性浅水引力波或潮汐波的一种特殊类型。

特别值得一提的是，这些图案与最近在驱动玻色-爱因斯坦凝聚态中发现的集体激发具有相似的特征，包括相同的平方根尺度色散和模式动力学以及类似的非线性特征，如硬弹簧非线性。基于这种紧密的对应关系，研究人员提出了受约束的经典和量子流体系统之间模式动力学的类比，并认为这种类比在非线性状态下也具有数学上的有效性。

据悉，自从在振动的流体层上发现卷曲现象以来，人们已经揭示出在流体表面上形成的许多不同类型的图案。

附：英文原文

Title: Polygonal patterns of Faraday water waves analogous to collective excitations in Bose–Einstein condensates

Author: Liu, Xinyun, Wang, Xinlong

Issue&Volume: 2023-12-07

Abstract: Since the discovery of crispations on a vibrating fluid layer, numerous types of patterns formed on fluid surfaces have been revealed. Here we report the observation of polygonal patterns of Faraday waves in vibrating water containers with parabolic and other concave bottoms. These patterns manifest themselves as simple geometric figures of symmetries ranging from elliptical up to heptagonal, with wavelengths much larger than the capillary length. Hence, they are intrinsically different from the previously studied patterns in vibrating drops or puddles and represent a particular variety of nonlinear shallow-water gravity waves or tidal waves in concave basins. Of specific interest is their resemblance to the collective excitations recently discovered in a driven Bose–Einstein condensate, not only sharing identical square-root scaling dispersion and pattern dynamics but also possessing similar nonlinear features like hard-spring nonlinearity. Based on the close correspondence, we propose an analogue of the patterning dynamics for classical and quantum fluid systems subject to confinement and argue that the analogy is mathematically valid even in the nonlinear regime.

DOI: 10.1038/s41567-023-02294-y

Source: https://www.nature.com/articles/s41567-023-02294-y