Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding or ‘pilot’ wave fields. These walking droplets, or ‘walkers’, exhibit several features previously thought to be peculiar to the microscopic, quantum realm. In particular, walkers confined to circular corrals manifest a wave-like statistical behaviour reminiscent of that of electrons in quantum corrals. Here we demonstrate that localized topological inhomogeneities in an elliptical corral may lead to resonant projection effects in the walker’s statistics similar to those reported in quantum corrals. Specifically, we show that a submerged circular well may drive the walker to excite specific eigenmodes in the bath that result in drastic changes in the particle’s statistical behaviour. The well tends to attract the walker, leading to a local peak in the walker’s position histogram. By placing the well at one of the foci, a mode with maxima near the foci is preferentially excited, leading to a projection effect in the walker’s position histogram towards the empty focus, an effect strongly reminiscent of the quantum mirage. Finally, we demonstrate that the mean pilot-wave field has the same form as the histogram describing the walker’s statistics.

毫米级的液滴可以在振动的液浴表面上行走，并通过与自己的引导波或“先导”波场的共振相互作用而自我推动。这些步行液滴或“步行者”展现出先前被认为是微观的量子领域特有的几个特征。尤其是，局限在圆形畜栏内的步行者表现出一种波状的统计行为，让人联想到量子级电子中的电子行为。在这里，我们证明椭圆形畜栏中的局部拓扑不均匀性可能导致沃克统计中的共振投影效应，类似于量子畜栏中报道的那些。具体而言，我们表明，一口浸没的圆形井可能会促使沃克在浴中激发特定的本征模式，从而导致粒子的统计行为发生剧烈变化。井往往会吸引步行者，从而导致步行者位置直方图中出现一个局部峰值。通过将孔放置在一个焦点上，将优先激发在焦点附近具有最大值的模式，从而导致步行者位置直方图中的投影效果朝着空焦点，这种效果强烈地使人联想到了海市rage楼。最后，我们证明了平均导波场具有与描述步行者统计数据的直方图相同的形式。