Pilot-Wave Hydrodynamics

这项研究将包括导波流体动力学的综合实验和理论研究，当液滴通过与其自身波场的共振相互作用沿振动流体槽表面推进时就会产生导波流体动力学。由Yves Couder在2005年发现的弹跳水滴系统，让人想起Louis de Broglie假设的量子动力学导波模型，认为它是哥本哈根解释的合理替代方案，并显示出几个曾经被认为是微观量子领域独有的特征，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似量子行为的产生方式。将特别注意演示在外力存在的情况下，导波动力学如何引起量子化状态，并最终产生具有波状统计的混沌轨迹。我们的起点将是对水滴在旋转的框架中和在存在中心力的情况下所产生的轨道解的稳定性分析。实验室实验将指导理论发展，并将探索新的量子模拟系统。一旦彻底了解了这个流体动力学系统的行为，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，它还将鼓励跨传统不同学科的交流，包括流体力学、量子物理和动力学系统的工作者之间的交流。爱因斯坦坚持认为，标准量子理论对微观粒子的统计描述是不完整的，并且建立在理性动力学的基础上。这种量子动力学的第一个项目是Louis de Broglie的导波理论，根据该理论，微观粒子在粒子内部振动产生的波场作用下运动。80多年后，也就是仅仅8年前，伊夫·库德发现了第一个导波系统，它是沿着振动液浴表面行走的毫米级水滴。值得注意的是，这些行走的水滴显示出许多被认为是微观世界所特有的特征。除了本身就是一个值得研究的丰富而微妙的动力系统外，行走的水滴还有可能洞察微观领域。这项研究将既探索问题，又揭示现代物理学的哲学基础。这项研究本质上是跨学科的，跨越流体力学、动力学系统和量子物理，因此将促进各领域之间新的联系的发展。

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.