论文标题
改良无序的klein-gordon晶格中正常模式的特性：从无序到秩序
Properties of normal modes in a modified disordered Klein-Gordon lattice: From disorder to order
论文作者
论文摘要
我们介绍了无序的Klein-Gordon晶格模型的修改版本，该模型具有两个用于控制疾病强度的参数：$ D $，它决定了现场电位的系数范围，以及$ W $，这定义了最近邻里相互作用的强度。我们修复了$ W = 4 $，并研究系统的正常模式的属性如何在接近其订购版本（即$ d \ rightarrow 0 $）时如何变化。我们表明，随着$ d $降低，普通模式的频率的概率密度分布会带来“ u”形的轮廓。此外，我们使用两个数量来估计模式的空间范围，所谓的本地化卷$ v $（这与模式的第二时刻有关）和模式的参与号$ p $。我们表明，当$ d $接近零时，两个量规模均为$ \ propto d^{ - 2} $，并且我们在数值上验证了它们之间的比例关系为$ v/p \约2.6 $。
We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: $D$, which determines the range of the coefficients of the on-site potentials, and $W$, which defines the strength of the nearest-neighbor interactions. We fix $W=4$ and investigate how the properties of the system's normal modes change as we approach its ordered version, i.e. $D\rightarrow 0$. We show that the probability density distribution of the normal modes' frequencies takes a `U'-shaped profile as $D$ decreases. Furthermore, we use two quantities for estimating the modes' spatial extent, the so-called localization volume $V$ (which is related to the mode's second moment) and the mode's participation number $P$. We show that both quantities scale as $\propto D^{-2}$ when $D$ approaches zero and we numerically verify a proportionality relation between them as $V/P \approx 2.6$.
