一维波粒体积分微分轨线方程中的类Lorenz系统
Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
摘要：
垂直振动液池可以在其自由表面上产生自推进的波粒实体。这个波粒实体的水平行走动力学可以通过积分-微分轨迹方程来充分描述。通过将一维波粒实体的积分-微分运动方程转化为一个常微分方程系统，我们证明了该实体的各种空间波形式的类洛伦兹动力学系统的出现。具体来说，我们提出并给出了洛伦兹动力系统的例子，出现时的波形梯度是（i）的线性齐次常系数ODE的解决方案，（ii）多项式和（iii）周期函数。理解类洛伦兹系统中的波粒实体的动力学，可能有助于从行走液滴的流体动力学量子模拟中的潜在混沌动力学中合理化涌现的统计行为。此外，这里提出的结果提供了一个替代物理解释的各种洛伦兹动力系统的波粒子实体的行走动力学。
英文摘要：
Vertically vibrating a liquid bath can give rise to a self-propelled wave-particle entity on its free surface. The horizontal walking dynamics of this wave-particle entity can be described adequately by an integro-differential trajectory equation. By transforming this integro-differential equation of motion for a one-dimensional wave-particle entity into a system of ordinary differential equations (ODEs), we show the emergence of Lorenz-like dynamical systems for various spatial wave forms of the entity. Specifically, we present and give examples of Lorenz-like dynamical systems that emerge when the wave form gradient is (i) a solution of a linear homogeneous constant coefficient ODE, (ii) a polynomial and (iii) a periodic function. Understanding the dynamics of the wave-particle entity in terms of Lorenz-like systems may provide to be useful in rationalizing emergent statistical behavior from underlying chaotic dynamics in hydrodynamic quantum analogs of walking droplets. Moreover, the results presented here provide an alternative physical interpretation of various Lorenz-like dynamical systems in terms of the walking dynamics of a wave-particle entity.
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