主动量子向列相：一次量子化
Active Quantum Nematics: The First Quantization
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中文总结 AI 辅助
该研究将主动向列相和液晶理论纳入量子力学框架，通过引入复值向列波函数实现。得到主动微游泳者的能量 - 频率关系、扩散趋化生物体的捕食者 - 猎物动力学，还能通过状态函数表征心脏，为相关研究提供了新方法。
中文摘要 AI 辅助
向列相对称性蕴含着诸如拓扑缺陷数和涡度单元等守恒量子化量。相应地，在主动向列相中发现了无数量子类比。我们通过将复值向列波函数引入贝里斯 - 爱德华兹方程，将主动向列相和液晶理论形式化到量子力学框架中，从而将时空变化的向列相系统分裂为量子化状态。由于控制方程的局部复相位对称性，我们得到了蠕动蠕虫和细菌等主动微游泳者的普朗克能量 - 频率关系。对于基于扩散趋化作用的生物体，我们得到了捕食者 - 猎物动力学，其演化以最大化/最小化信息素场梯度重叠。此外，在对跳动心脏进行量子化时，类似于氢原子轨道，状态函数使我们不仅能通过节律，还能通过健康和不健康心脏中各种谐波收缩活动的时空分布来表征心脏。
英文摘要
Nematic symmetry entails conserved quantized quantities such as number of topological defects and vorticity cells. Correspondingly, countless quantum analogies have been found in Active Nematics. We formalize Active Nematics and Liquid Crystal theory into the framework of Quantum Mechanics by introducing a complex valued Nematic Wavefunction to the Beris Edward equations, thus splitting spatiotemporally varying nematic systems into quantized states. We obtain the Planck's energy-frequency relationship for active micro-swimmers such as peristaltic worms and bacterium as a consequence of local complex phase-symmetry of the governing equations, similar to the gauge formulation of Electromagnetism. For organisms operating on diffusive chemotaxis, we obtain predator-prey dynamics that evolve to maximize/minimize pheromones field gradient overlap. Furthermore, when quantizing beating hearts, similar to the orbitals of hydrogen atoms, the state-function allows us to characterize hearts not only through the rhythm, but also the spaciotemporal distribution of contractile activity of various harmonics among healthy and unhealthy hearts.
