James Franck Institute and Department of Physics, University of Chicago, Chicago, IL, USA.
Department of Physics, Osaka University, Toyonaka, Japan.
Nature. 2021 Apr;592(7854):363-369. doi: 10.1038/s41586-021-03375-9. Epub 2021 Apr 14.
Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter, non-equilibrium systems, networks of neurons, social groups with conformist and contrarian members, directional interface growth phenomena and metamaterials. Although wave propagation in non-reciprocal media has recently been closely studied, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points. We describe the emergence of these phases using insights from bifurcation theory and non-Hermitian quantum mechanics. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.
失去平衡时，缺乏互惠关系是常态而非例外。互惠关系缺失的情况出现在主动物质、非平衡系统、神经元网络、存在从众和异议成员的社会团体、具有方向性的界面生长现象和超材料中。尽管最近对非互易介质中的波传播进行了密切研究，但对于非互易性对多体系统集体行为的影响知之甚少。在这里，我们表明非互易性会导致时间相关的相位，其中自发破缺的连续对称性会被动态恢复。我们用简单的机器人演示来说明这一机制。这些相变由称为异常点的谱奇异点控制。我们使用分岔理论和非厄米量子力学的见解来描述这些相位的出现。我们的方法捕捉到了非互易性对三种典型自组织的扩展：同步、群集和模式形成。这些系统中的集体现象从主动时间（准）晶体到异常点强制模式形成和滞后。我们的工作为非优化原理控制动力学的系统中的临界现象的一般理论奠定了基础。
