Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the random landscape. In stark contrast, wave-particle duality causes electrons in disordered media to come to rest even when the potential is weak—a remarkable phenomenon known as Anderson localization. Here, we present a hydrodynamic active system with wave-particle features, a millimetric droplet self-guided by its own wave field over a submerged random topography, whose dynamics exhibits localized statistics analogous to those of electronic systems. Consideration of an ensemble of particle trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography. We rationalize mechanistically the emergent statistics by virtue of the wave-mediated resonant coupling between the droplet and topography, which produces an attractive wave potential about the localization region. This hydrodynamic analog, which demonstrates how a classical particle may localize like a wave, suggests new directions for future research in various areas, including active matter, wave localization, many-body localization, and topological matter.

中文翻译：

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行走液滴的 Anderson 定位


了解粒子在无序环境中机动的能力是无数环境中的核心问题，从活性物质和生物学到电子学。当宏观粒子的能量超过随机景观的特征势垒时，它们最终会表现出扩散运动。与此形成鲜明对比的是，波粒二象性导致无序介质中的电子即使在电位较弱时也会静止——这种显着现象被称为安德森定位。在这里，我们提出了一个具有波粒特征的流体动力学有源系统，一个毫米级液滴在水下随机地形上由自己的波场自导，其动力学表现出类似于电子系统的局部统计数据。考虑粒子轨迹的集合表明，当导流波场延伸到无序地形上时，扩散会受到抑制。我们利用液滴和地形之间的波介导共振耦合，从机械上合理化了涌现统计量，这在定位区域产生了有吸引力的波势。这个流体动力学模拟展示了经典粒子如何像波一样定位，为各个领域的未来研究提出了新的方向，包括活性物质、波定位、多体定位和拓扑物质。