Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Chaos. 2020 Oct;30(10):103115. doi: 10.1063/5.0020775.
A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating fluid bath, guided by its self-generated wave field. This hydrodynamic pilot-wave system exhibits a vast range of dynamics, including behavior previously thought to be exclusive to the quantum realm. We present the results of a theoretical investigation of an idealized pilot-wave model, in which a particle is guided by a one-dimensional wave that is equipped with the salient features of the hydrodynamic system. The evolution of this reduced pilot-wave system may be simplified by projecting onto a three-dimensional dynamical system describing the evolution of the particle velocity, the local wave amplitude, and the local wave slope. As the resultant dynamical system is remarkably similar in form to the Lorenz system, we utilize established properties of the Lorenz equations as a guide for identifying and elucidating several pilot-wave phenomena, including the onset and characterization of chaos.
毫米大小的液滴可能会在垂直振动的液体浴表面上反弹并自行推进，这是由其自生的波场引导的。这个流体动力导波系统表现出广泛的动力学行为，包括以前被认为是量子领域独有的行为。我们提出了对理想化导波模型的理论研究结果，其中一个粒子被一个一维波引导，这个一维波具有该流体动力系统的显著特征。通过将这个简化的导波系统投影到一个描述粒子速度、局部波幅和局部波斜率演化的三维动力系统上，可以简化这个系统的演化。由于这个结果动力系统在形式上与洛伦兹系统非常相似，我们利用洛伦兹方程的已有性质作为指导，来识别和阐明几个导波现象，包括混沌的出现和特征。
