偶极链中的能量传递机制：从能量均分到呼吸子的形成
Energy transfer mechanisms in a dipole chain: From energy equipartition to the formation of breathers
摘要：
研究了$N$相互作用刚性旋转偶极子的经典偶极子链中的能量传递。特别是通过确定平衡点及其在共同旋转平面中的稳定性，分析了潜在的高维势能景观。从最小能量组态出发，研究了链对单个偶极子激发的响应。利用偶极链的线性化和精确的哈密顿量，我们检测到一个近似的激发能阈值之间的弱和强非线性动力学。在弱非线性状态下，随着时间的推移，链接近偶极子之间的预期能量均分。对于较高能量的激发，出现强烈的局部激发，其时间轨迹是周期性的或不规则的，分别与众所周知的离散或混沌呼吸子有关。发现混沌呼吸子的时间演化过程中普遍存在自发形成相反极化畴和锁相畴的现象。最后，通过计算一个快速混沌指标，研究了偶极链动力学对初始条件的敏感性随初始激发能的变化。这项研究的结果证实了上述近似阈值的初始激发能，低于该值的偶极链的动力学是规则的，高于该值是混乱的。
英文摘要：
We study the energy transfer in a classical dipole chain of $N$ interacting rigid rotating dipoles. The underlying high--dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonlinear regime, the chain approaches in the course of time the expected energy equipartition among the dipoles. For excitations of higher energy, strongly localized excitations appear whose trajectories in time are either periodic or irregular, relating to the well-known discrete or chaotic breathers, respectively. The phenomenon of spontaneous formation of domains of opposite polarization and phase locking is found to commonly accompany the time evolution of the chaotic breathers. Finally, the sensitivity of the dipole chain dynamics to the initial conditions is studied as a function of the initial excitation energy by computing a fast chaos indicator. The results of this study confirm the aforementioned approximate threshold value for the initial excitation energy, below which the dynamics of the dipole chain is regular and above which it is chaotic.
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