论文标题
在经典波粒子实体的洛伦兹样系统中的动力学，干扰效应和多稳定性
Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave-particle entity in a periodic potential
论文作者
论文摘要
经典的波颗粒实体（WPE）可以通过实验实现，因为液滴在垂直振动的液态浴的自由表面上行走，液滴的水平步行运动以其自生成的波场引导。这些自构的WPE已显示出表现出几种量子和光学现象的类似物。使用理想化的理论模型，采用类似洛伦兹的系统的形式，我们从理论上和数字上探索了正弦电位中这种一维WPE的动力学。我们发现系统的稳态状态与固定的WPE以及一系列不稳定的动作相对应，例如来回振荡的步行者，失控的振荡步行者和各种类型的不规则步行者。在由应用正弦电位的无量纲参数形成的参数空间中，我们观察到交替的不稳定行为的模式表明干扰效应。此外，在参数空间的某些区域中，我们还确定了粒子长期行为中取决于初始条件的多稳定性。我们在WPE系统中确定的行为与Bragg的光反射以及晶体中的电子运动之间进行类比。
A classical wave-particle entity (WPE) can be realized experimentally as a droplet walking on the free surface of a vertically vibrating liquid bath, with the droplet's horizontal walking motion guided by its self-generated wave field. These self-propelled WPEs have been shown to exhibit analogs of several quantum and optical phenomena. Using an idealized theoretical model that takes the form of a Lorenz-like system, we theoretically and numerically explore the dynamics of such a one-dimensional WPE in a sinusoidal potential. We find steady states of the system that correspond to a stationary WPE as well as a rich array of unsteady motions such as back-and-forth oscillating walkers, runaway oscillating walkers and various types of irregular walkers. In the parameter space formed by the dimensionless parameters of the applied sinusoidal potential, we observe patterns of alternating unsteady behaviors suggesting interference effects. Additionally, in certain regions of the parameter space, we also identify multistability in the particle's long-term behavior that depends on the initial conditions. We make analogies between the identified behaviors in the WPE system and Bragg's reflection of light as well as electron motion in crystals.
