偶极链中的稳定和不稳定轨道
Stable and unstable trajectories in a dipolar chain
摘要：
在经典力学中，解可以根据其稳定性进行分类。它们中的每一个都是系统可能轨迹的一部分。然而，不稳定解的特征在实验中很难观察到，而且大多数时候，如果实验实现是绝热的，它们被认为只是一个麻烦。在这里，我们使用少量的XY磁偶极子受到外部磁场的研究起源，他们的集体磁响应。利用分歧理论，我们已经找到了所有可能的解决方案是稳定的或不稳定的，并探讨了这些解决方案是如何自然连接的点，系统的对称性丢失或恢复。不稳定的解决方案，揭示了系统的对称性被发现是在这个系统中的形状磁滞回线的罪魁祸首。利用边界盆地熵的概念分析了非线性动力学解的复杂性，发现阻尼时间尺度对吸引盆地中分形结构的出现至关重要.此外，我们通过数值计算找到了畴壁解，这些畴壁解是磁性中横向壁和涡旋壁的最小可能实现。我们的实验证实了它们的存在和稳定性，表明我们的系统是一个合适的平台，在宏观尺度上研究畴壁动力学。
英文摘要：
In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most of the times if the experimental realization is adiabatic, they are considered just a nuisance. Here we use a small number of XY magnetic dipoles subject to an external magnetic field for studying the origin of their collective magnetic response. Using bifurcation theory we have found all the possible solutions being stable or unstable, and explored how those solutions are naturally connected by points where the symmetries of the system are lost or restored. Unstable solutions that reveal the symmetries of the system are found to be the culprit that shape hysteresis loops in this system. The complexity of the solutions for the nonlinear dynamics is analyzed using the concept of boundary basin entropy, finding that the damping time scale is critical for the emergence of fractal structures in the basins of attraction. Furthermore, we numerically found domain wall solutions that are the smallest possible realizations of transverse walls and vortex walls in magnetism. We experimentally confirmed their existence and stability showing that our system is a suitable platform to study domain wall dynamics at the macroscale.
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