论文标题
二维无序磁超材料
A two-dimensional disordered magnetic metamaterial
论文作者
论文摘要
我们研究了谐振频率障碍对本征状态的影响以及在二维（平方）分裂谐振器（SRRS）中磁能的运输。在没有障碍的情况下，我们发现磁性波和均方根位移（MSD）的分散关系以封闭形式的形式，表明长期以来，MSD是弹道的。当存在障碍时，我们会考虑两种类型：通常的安德森分布（不相关的单体）和$ 2 \ times 2 $单位，以随机分配给晶格站点（相关的四聚体）。这是一维随机二聚体模型（RDM）的两个维度的直接扩展。对于不相关的情况，我们看到MSD在所有疾病宽度中都饱和，而对于相关的情况，我们找到了一个疾病窗口，其中MSD在长时间内不饱和，并具有渐近的亚避免行为$ MSD \ MSD \ sim t^{0.26} $。在此疾病窗口外，MSD显示出与单体情况相同的饱和度。我们猜想，降低的行为是对跨四聚体单元的2D平面波的较弱的谐振传递的遗迹。
We study the effect of a resonant frequency disorder on the eigenstates and the transport of magnetic energy in a two-dimensional (square) array of split-ring resonators (SRRs). In the absence of disorder, we find the dispersion relation of magneto-inductive waves and the mean square displacement (MSD) in closed form, showing that at long times the MSD is ballistic. When disorder is present, we consider two types: the usual Anderson distribution (uncorrelated monomers) and $2 \times 2$ units assigned at random to lattice sites (correlated tetramers). This is a direct extension to two dimensions of the one-dimensional random dimer model (RDM). For the uncorrelated case, we see saturation of the MSD for all disorder widths, while for the correlated case we find a disorder window, inside which the MSD does not saturate at long times, with an asymptotic sub-diffusive behavior $MSD\sim t^{0.26}$. Outside this disorder window, the MSD shows the same kind of saturation as in the monomer case. We conjecture that the sub-diffusive behavior is a remanent of a weak resonant transmission of a 2D plane wave across a tetramer unit.
