We examine the transport of magnetic energy in a simplified model of a magnetic metamaterial, consisting of a one-dimensional array of split-ring resonators, in the presence of correlated disorder in the resonant frequencies. The computation of the average participation ratio (PR) reveals that on average, the modes for the correlated disorder system are less localized than in the uncorrelated case. The numerical computation of the mean square displacement of an initially localized magnetic excitation for the correlated case shows a substantial departure from the uncorrelated (Anderson-like) case. A long-time asymptotic fit $\langle n^2\rangle \sim t^\alpha$ reveals that, for the uncorrelated system $\alpha\sim 0$, while for the correlated case $\alpha>0$, spanning a whole range of behavior ranging from localization to super-diffusive behavior. The transmission coefficient of a plane wave across a single magnetic dimer reveals the existence of well-defined regions in disorder strength-magnetic coupling space, where unit transmission for some wavevector(s) is possible. This implies, according to the random dimer model (RDM) of Dunlap et al., a degree of mobility. A comparison between the mobilities of the correlated SRR system and the RDM shows that the RDM model has better mobility at low disorder while our correlated SRR model displays better mobility at medium and large disorder.

中文翻译：

---

具有相关紊乱的磁性超材料

我们研究了磁性超材料的简化模型中的磁能传输，该模型由一维开环谐振器阵列组成，在谐振频率存在相关无序的情况下。平均参与率 (PR) 的计算表明，平均而言，相关无序系统的模式比不相关情况下的局部化程度更低。相关情况下初始局部磁激励的均方位移的数值计算表明与不相关（类似安德森）的情况有很大的不同。长时间渐近拟合 $\langle n^2\rangle \sim t^\alpha$ 表明，对于不相关系统 $\alpha\sim 0$，而对于相关情况 $\alpha>0$，跨越一个从定位到超扩散行为的整个行为范围。平面波穿过单个磁二聚体的传输系数揭示了在无序强度-磁耦合空间中存在明确定义的区域，其中某些波向量的单位传输是可能的。根据 Dunlap 等人的随机二聚体模型 (RDM)，这意味着一定程度的流动性。相关 SRR 系统和 RDM 的迁移率之间的比较表明，RDM 模型在低无序时具有更好的迁移率，而我们的相关 SRR 模型在中、大无序时显示出更好的迁移率。一定程度的流动性。相关 SRR 系统和 RDM 的迁移率之间的比较表明，RDM 模型在低无序时具有更好的迁移率，而我们的相关 SRR 模型在中、大无序时显示出更好的迁移率。一定程度的流动性。相关 SRR 系统和 RDM 的迁移率之间的比较表明，RDM 模型在低无序时具有更好的迁移率，而我们的相关 SRR 模型在中、大无序时显示出更好的迁移率。