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.

中文翻译：

---

经典导波动力学中的速度振荡

我们展示了一个动力学系统的理论研究结果，该系统由一个粒子通过与它自己的准单色引导波场的共振相互作用自推进。我们将两种不同的机制合理化，它们出现在参数空间的不同区域，可能会导致具有导频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，可能会出现与引导波波长的共振速度振荡。其次，当引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。讨论了经典导频波系统中涌现统计的含义。