标题： 多群体系统中的广义非互易相变 显示英文标题

标题： Generalized non-reciprocal phase transitions in multipopulation systems

摘要： 非互惠相互作用在各种复杂系统中普遍存在，导致传统平衡统计物理无法描述的现象。 尽管由两组分组成的非互惠相互作用系统已被深入研究，但具有任意数量组分的非互惠系统的物理性质尚未得到充分探索，尽管其对生物系统、活性物质和驱动耗散量子材料可能具有重要意义。 在本工作中，我们研究了在多个非互惠耦合组分的$O(2)$对称多体系统中出现的相和相变的普遍特征，适用于微观模型，如振荡器网络、群体运动模型，以及更一般的情况，其中每个代理都有一个相变量。 通过利用可能轨道的对称性和拓扑结构，我们系统地展示了多种时间依赖相和相变的出现。 例如包括多组分手性相，这些相与其两组分对应相不同，通过由临界例外点表征的相变出现，以及极限环鞍点分支和霍普夫分支。 有趣的是，我们发现一种动态恢复$\mathbb{Z}_2$对称性的相变是通过同宿轨道分支发生的，在相变点处两个$\mathbb{Z}_2$破缺轨道合并，为$N\geq4$组分的序参量动力学提供了同宿混沌的一般途径。 结果有助于理解新型集体行为，并为分类由非互惠相互作用驱动的系统的动态相及其转变提供了形式化方法。 显示英文摘要

摘要： Non-reciprocal interactions are prevalent in various complex systems leading to phenomena that cannot be described by traditional equilibrium statistical physics. Although non-reciprocally interacting systems composed of two populations have been closely studied, the physics of non-reciprocal systems with a general number of populations is not well explored despite the potential relevance to biological systems, active matter, and driven-dissipative quantum materials. In this work, we investigate the generic features of the phases and phase transitions that emerge in $O(2)$ symmetric many-body systems with multiple non-reciprocally coupled populations, applicable to microscopic models such as networks of oscillators, flocking models, and more generally systems where each agent has a phase variable. Using symmetry and topology of the possible orbits, we systematically show that a rich variety of time-dependent phases and phase transitions arise. Examples include multipopulation chiral phases that are distinct from their two-population counterparts that emerge via a phase transition characterized by critical exceptional points, as well as limit cycle saddle-node bifurcation and Hopf bifurcation. Interestingly, we find a phase transition that dynamically restores the $\mathbb{Z}_2$ symmetry occurs via a homoclinic orbit bifurcation, where the two $\mathbb{Z}_2$ broken orbits merge at the phase transition point, providing a general route to homoclinic chaos in the order parameter dynamics for $N\geq4$ populations. The results contribute to the understanding of the novel collective behavior and provide formalism for classifying dynamic phases and their transitions in systems driven by non-reciprocal interactions.