所谓混沌状态的减速：“冻结”初始状态
Slowing down of so-called chaotic states: "Freezing" the initial state
摘要：
分析了$XY$在规则临界范围网络上相互作用的模型中出现的所谓混沌状态。典型的时间尺度提取的时间序列分析的全球磁化。大的光谱证实了可观测的混沌性质，无论如何，光谱中不同的峰允许出现典型的特征时间尺度。我们发现这些时间尺度$τ(N)$显示出临界的慢化，即它们发散为$N\rightarrow\infty$。对不同能量密度下的标度律进行了分析，展示了$τ(N)\sim\sqrt{N}$的行为。这种行为进一步解释分析使用的运动方程的形式主义和分析的邻接矩阵的特征值。
英文摘要：
The so-called chaotic states that emerge on the model of $XY$ interacting on regular critical range networks are analyzed. Typical time scales are extracted from the time series analysis of the global magnetization. The large spectrum confirms the chaotic nature of the observable, anyhow different peaks in the spectrum allows for typical characteristic time-scales to emerge. We find that these time scales $τ(N)$ display a critical slowing down, i.e they diverge as $N\rightarrow\infty$. The scaling law is analyzed for different energy densities and the behavior $τ(N)\sim\sqrt{N}$ is exhibited. This behavior is furthermore explained analytically using the formalism of thermodynamic-equations of the motion and analyzing the eigenvalues of the adjacency matrix.
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