Pilot-Wave Hydrodynamics

这项研究将包括对导波流体动力学的综合实验和理论研究，当液滴通过与自身波场的共振相互作用推动自己沿着振动液浴表面时，就会出现导波流体动力学。由伊夫·库德于2005年发现的弹跳液滴系统，让人想起了由路易·德布罗意提出的量子动力学的导波模型，该模型是哥本哈根解释的一个合理选择，并表现出一些曾经被认为是微观量子领域所独有的特征，包括隧道效应、轨道量子化和波状统计。这项研究将致力于阐明这种类量子行为产生的方式。将特别注意演示在外力存在下的导波动力学如何产生量子化状态，并最终产生具有波状统计的混沌轨迹。起点将是在中心力存在的情况下，对在旋转框架中行走的液滴所产生的轨道解进行稳定性分析。实验室实验将指导理论发展，并探索新的量子模拟系统。一旦这个流体动力系统的行为被彻底理解，我们将研究弹跳液滴和量子粒子之间的联系，它们的统计和动力学。除了这项研究对研究生和本科生的直接教育价值外，它还将鼓励流体动力学、量子物理学和动力系统工作者之间在传统上不同学科之间的交流。爱因斯坦坚持认为，标准量子理论提供的微观粒子的统计描述是不完整的，并以理性动力学为基础。这种量子动力学的第一个项目是路易·德布罗意的导航波理论，根据该理论，微观粒子会对粒子内部振动产生的波场做出反应。80多年后，也就是8年前，伊夫·库德（Yves Couder）发现了第一个导航波系统，其形式是毫米级的液滴沿着振动液浴的表面移动。值得注意的是，这些行走的液滴表现出许多被认为是微观世界特有的特征。除了作为一个丰富而微妙的动力系统本身值得研究外，行走的液滴还具有洞察微观领域的潜力。这项研究将探索现代物理学的问题和哲学基础。这项研究本质上是跨学科的，跨越了流体动力学、动力系统和量子物理学，因此将促进各领域之间新联系的发展。

This research will be comprised of an integrated experimental and theoretical investigation of pilot-wave hydrodynamics, as arises when droplets propel themselves along the surface of a vibrating fluid bath through resonant interaction with their own wave field. Discovered by Yves Couder in 2005, the bouncing droplet system is reminiscent of the pilot-wave model of quantum dynamics postulated by Louis de Broglie as a rational alternative to the Copenhagen Interpretation, and exhibits several features once thought to be exclusive to the microscopic, quantum realm, including tunneling, orbital quantization and wavelike statistics. The research will be directed towards elucidating the manner in which this quantum-like behavior arises. Particular attention will be given to demonstrating how pilot-wave dynamics in the presence of an external force gives rise to quantized states, and ultimately to chaotic trajectories with wave-like statistics. The starting point will be a stability analysis of orbital solutions arising for drops walking in a rotating frame, and in the presence of a central force. Laboratory experiments will guide the theoretical developments, and new quantum analog systems will be explored. Once the behavior of this hydrodynamic system is thoroughly understood, we will investigate the link between the bouncing droplets and quantum particles, their statistics and dynamics. In addition to the direct educational value of this research to the graduate and undergraduate students involved, it will encourage communication across traditionally disparate disciplines, between workers in fluid dynamics, quantum physics and dynamical systems.Einstein insisted that the statistical description of microscopic particles provided by standard quantum theory is incomplete, and underlaid by a rational dynamics. The first project for such a quantum dynamics was the pilot-wave theory of Louis de Broglie, according to which microscopic particles move in responseto a wave field generated by the particle's internal vibration. More than 80 years later, only 8 years ago, the first pilot-wave system was discovered by Yves Couder, in the form of millimetric drops walking along the surface of a vibrating fluid bath. Remarkably, these walking droplets exhibit many features thought to be peculiar to the microscopic world. In addition to being a rich and subtle dynamical system worthy of study in its own right, the walking droplets have the potential to yield insight into the microscopic realm. This research will explore both question and inform the philosophical foundations of modern physics. This research is interdisciplinary in nature, spanning fluid dynamics, dynamical systems and quantum physics, so will foster the development of new links between fields.