Schrödinger Dynamics and Berry Phase of Undulatory Locomotion
Schrödinger Dynamics and Berry Phase of Undulatory Locomotion
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薛定谔动力学和波动运动的贝里相
DOI：
10.1103/physrevlett.130.258402
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发表时间：
2023
影响因子：
8.6
通讯作者：
Dunkel, Jörn
中科院分区：
文献类型：
--
作者：
Cohen, Alexander E.;Hastewell, Alasdair D.;Pradhan, Sreeparna;Flavell, Steven W.;Dunkel, Jörn
谱模式表示在从量子力学到流体湍流的各个物理学领域中发挥着重要作用，但它们尚未广泛用于表征和描述生命系统的行为动力学。在这里，我们表明，从实验实时成像数据推断出的基于模式的线性模型可以提供蠕虫、蜈蚣、机器人和蛇的波动运动的准确低维描述。通过将物理对称性和已知的生物约束纳入动力学模型，我们发现形状动力学通常由模态空间中的薛定谔方程控制。有效生物物理哈密顿量的本征态及其绝热变化使得能够使用格拉斯曼距离和贝里相位对自然、模拟和机器人有机体中的运动行为进行有效分类和区分。虽然我们的分析侧重于广泛研究的一类生物物理运动现象，但基本方法可推广到允许模式表示受几何形状约束的其他物理或生命系统。
Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.