We predict a new type of two- and three-dimensional stable quantum droplets persistently rotating in broad external two-dimensional and weakly anharmonic potential. Their evolution is described by the system of the Gross-Pitaevskii equations with Lee-Huang-Yang quantum corrections. Such droplets resemble whispering-gallery modes localized in the polar direction due to nonlinear interactions and, depending on their chemical potential and rotation frequency, they appear in rich variety of shapes, ranging from nearly flat-top or strongly localized rotating wave packets, to crescentlike objects extending nearly over the entire range of polar angles. Above critical rotation frequency quantum droplets transform into vortex droplets (in two dimensions) or vortex tori (in three dimensions), whose topological charge gradually increase with the increase of the modulus of chemical potential, and therefore they belong to the family of nonlinear modes connecting fundamental and vortex quantum droplets. Rotating quantum droplets are exceptionally robust objects, stable practically in the entire range of their existence.

中文翻译：

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旋转多维量子液滴

我们预测了一种新型的二维和三维稳定量子液滴，该液滴在广泛的外部二维弱非谐势中持续旋转。它们的演化由具有 Lee-Huang-Yang 量子校正的 Gross-Pitaevskii 方程系统描述。由于非线性相互作用，这种液滴类似于位于极地方向的回音壁模式，并且根据它们的化学势和旋转频率，它们呈现出丰富多样的形状，从近乎平顶或强局域化的旋转波包到新月状几乎在整个极角范围内延伸的物体。高于临界旋转频率的量子液滴转变为涡流液滴（二维）或涡环（三维），其拓扑电荷随着化学势模量的增加而逐渐增加，因此它们属于连接基本和涡旋量子液滴的非线性模式族。旋转的量子液滴是非常坚固的物体，在其存在的整个范围内几乎都是稳定的。