Durey Matthew, Turton Sam E, Bush John W M
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Proc Math Phys Eng Sci. 2020 Jul;476(2239):20190884. doi: 10.1098/rspa.2019.0884. Epub 2020 Jul 22.
We present the results of a theoretical investigation of a dynamical system consisting of a particle self-propelling through a resonant interaction with its own quasi-monochromatic pilot-wave field. We rationalize two distinct mechanisms, arising in different regions of parameter space, that may lead to a wavelike statistical signature with the pilot-wavelength. First, resonant speed oscillations with the wavelength of the guiding wave may arise when the particle is perturbed from its steady self-propelling state. Second, a random-walk-like motion may set in when the decay rate of the pilot-wave field is sufficiently small. The implications for the emergent statistics in classical pilot-wave systems are discussed.
我们展示了一个动力学系统的理论研究结果，该系统由一个通过与其自身准单色导波场的共振相互作用进行自推进的粒子组成。我们阐述了在参数空间的不同区域出现的两种不同机制，它们可能导致具有导波波长的波状统计特征。首先，当粒子从其稳定的自推进状态受到扰动时，可能会出现与导波波长共振的速度振荡。其次，当导波场的衰减率足够小时，可能会出现类似随机游走的运动。我们还讨论了这些结果对经典导波系统中出现的统计现象的影响。
