Supplementary material.zip from Speed oscillations in classical pilot-wave dynamics

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.

本研究报告了一项动力学系统的理论探究成果，该系统由通过与自身准单色导波场（pilot-wave field）发生共振相互作用实现自主推进的粒子构成。本研究阐释了两种分别存在于不同参数空间区域的独特机制，这些机制可催生与导波波长相关的类波统计特征：其一，当粒子偏离其稳定自主推进状态并受到扰动时，会出现与导波波长匹配的共振速度振荡现象；其二，当导波场的衰减率足够低时，会出现类随机游走运动。本研究还探讨了上述结论对经典导波系统中涌现统计特征的启示意义。