Pilot-Wave Hydrodynamics

这项研究将包括一个综合的实验和理论研究的先导波流体动力学，产生时，液滴推动自己沿着表面的振动流体浴通过共振相互作用与自己的波场。Yves Couder在2005年发现的弹跳液滴系统让人想起了Louis de布罗意提出的量子动力学的导波模型，作为哥本哈根解释的合理替代方案，并展示了一些曾经被认为是微观量子领域独有的特征，包括隧道效应，轨道量子化和波动统计。这项研究将致力于阐明这种类似量子的行为产生的方式。特别注意将给予演示如何在外力的存在下，导频波动力学引起的量子化状态，并最终到混沌轨道与波一样的统计。 出发点将是一个稳定性分析的轨道解决方案所产生的液滴行走在一个旋转的框架，并在存在一个中心力。实验室实验将指导理论发展，并将探索新的量子模拟系统。一旦这个流体动力学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。除了对研究生和本科生的直接教育价值外，这项研究还将鼓励流体动力学、量子物理学和动力学系统等传统学科之间的交流。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·德布罗意布罗意的导波理论，根据该理论，微观粒子的运动是对粒子内部振动产生的波场的响应。80多年后，仅仅8年前，Yves Couder发现了第一个导频波系统，其形式是沿着振动液体浴表面行走的毫米级液滴。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所特有的特征。除了是一个丰富而微妙的动力系统值得研究本身，步行液滴有潜力产生洞察微观领域。这项研究将探索现代物理学的哲学基础。这项研究是跨学科的性质，跨越流体动力学，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.