非互易阻挫：时间晶体序由无序现象与类自旋玻璃态
Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
AI总结：
本文通过建立非互易相互作用系统与几何阻挫系统之间的直接类比，揭示了噪声或无序可解除轨道偶然简并并诱导自发对称性破缺，并发现非互易性诱导的类自旋玻璃态，为理解非互易物质提供了新视角。
摘要：
活性系统由相互作用本质上普遍具有非互易性的组分构成。这种非互易性常常导致存在相互冲突目标的情形，例如捕食者追逐猎物而猎物试图逃脱捕获的情形。这种情形在某种程度上让人联想到几何阻挫系统中遇到的情况，在那些系统中同样存在相互冲突的目标，从而导致不存在能够同时最小化所有相互作用能量的构型。在后者中，已知由于基态的偶然简并性会产生丰富多样的奇异现象。在本文中，我们在上述两类系统之间建立了直接的类比。该类比基于如下观察：具有反对称耦合的非互易相互作用系统与几何阻挫系统有一个共同点，即二者都表现出边缘轨道，这些边缘轨道可被视为偶然简并基态在动力系统中的对应物。前者通过证明一个刘维尔型定理得以展示。研究表明，这些轨道的“偶然简并性”常常会因涌现的“熵力”而被随机噪声或弱随机无序“解除”，从而产生噪声诱导的自发对称性破缺，其方式类似于几何阻挫系统中已知的序由无序现象。此外，我们报告了数值证据，证明存在一种由非互易性诱导的类自旋玻璃态，该态表现出短程空间关联（呈拉伸指数衰减）以及与老化效应相关的代数时间关联。我们的工作建立了复杂磁性材料物理与非互易物质之间意想不到的联系，为理解后者提供了新颖而有价值的视角。
英文摘要：
Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing its prey, while the prey attempts to evade capture. This situation is somewhat reminiscent of those encountered in geometrically frustrated systems where conflicting objectives also exist, which result in the absence of configurations that simultaneously minimize all interaction energies. In the latter, a rich variety of exotic phenomena are known to arise due to the presence of accidental degeneracy of ground states. In this paper, we establish a direct analogy between these two classes of systems. The analogy is based on the observation that non-reciprocally interacting systems with anti-symmetric coupling and geometrically frustrated systems have in common that they both exhibit marginal orbits, which can be regarded as a dynamical system counterpart of accidentally degenerate ground states. The former is shown by proving a Liouville-type theorem. These ''accidental degeneracies'' of orbits are shown to often get ''lifted'' by stochastic noise or weak random disorder due to the emergent ''entropic force'' to give rise to a noise-induced spontaneous symmetry breaking, in a similar manner to the order-by-disorder phenomena known to occur in geometrically frustrated systems. Furthermore, we report numerical evidence of a non-reciprocity-induced spin-glass-like state that exhibits a short-ranged spatial correlation (with stretched exponential decay) and an algebraic temporal correlation associated with the aging effect. Our work establishes an unexpected connection between the physics of complex magnetic materials and non-reciprocal matter, offering a fresh and valuable perspective for comprehending the latter.
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