论文标题
分数安德森模型
A fractional Anderson model
论文作者
论文摘要
我们检查了一维紧密结合的安德森模型中疾病与部分之间的相互作用。在没有疾病的情况下，我们观察到，两个最低的能量特征值从频段的底部脱离了自己，因为分级性$ s $的减少，在$ s = 0 $下完全退化，共同的能量等于半带宽，$ v $。其余的$ N-2 $状态完全退化，形成了一个平坦的频带，其能量等于带宽，$ 2V $。因此，在基态和频带之间形成了差距。在存在障碍和固定障碍宽度的情况下，$ s $的减少会降低点光谱的宽度，而对于固定的$ s $，疾病的增加会增加光谱的宽度。对于所有疾病宽度，平均参与率均以$ S $降低，呈现出本地化的趋势。但是，平均均方根位移（MSD）显示出低$ s $值的驼峰，表明存在扩展状态的存在，这与远程跳跃模型中发现的一致。
We examine the interplay between disorder and fractionality in a one-dimensional tight-binding Anderson model. In the absence of disorder, we observe that the two lowest energy eigenvalues detach themselves from the bottom of the band, as fractionality $s$ is decreased, becoming completely degenerate at $s=0$, with a common energy equal to a half bandwidth, $V$. The remaining $N-2$ states become completely degenerate forming a flat band with energy equal to a bandwidth, $2V$. Thus, a gap is formed between the ground state and the band. In the presence of disorder and for a fixed disorder width, a decrease in $s$ reduces the width of the point spectrum while for a fixed $s$, an increase in disorder increases the width of the spectrum. For all disorder widths, the average participation ratio decreases with $s$ showing a tendency towards localization. However, the average mean square displacement (MSD) shows a hump at low $s$ values, signaling the presence of a population of extended states, in agreement with what is found in long-range hopping models.
