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.
