Department of Electrical Engineering, Princeton University, New Jersey 08544, USA.
Phys Rev Lett. 2012 Aug 17;109(7):076402. doi: 10.1103/PhysRevLett.109.076402. Epub 2012 Aug 16.
We observe an apparent singularity in the electronic properties of the Anderson model of localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that occurs in dimensions d > 2. We present results of numerical calculations for Anderson's original uniform (box) distribution of on-site disorder in dimensions d = 1, 2, and 3. To establish this hitherto unreported behavior, and to understand its evolution with disorder, we contrast the behavior of two different measures of the localization length of the electronic wave functions-the averaged inverse participation ratio and the Lyapunov exponent. Our data suggest that Anderson's model exhibits richer behavior than has been established so far.
我们观察到局域化的安德森模型在有界对角无序下的电子性质中出现了明显的奇点，这与在维度 d > 2 时发生的、已经确立的迁移率边（局域化-去局域化转变）明显不同。我们给出了安德森原始均匀（盒）局域无序在维度 d = 1、2 和 3 中的数值计算结果。为了确定这种迄今为止尚未报道的行为，并了解其随无序的演化，我们对比了两种不同的电子波函数局域长度度量的行为——平均逆参与比和 Lyapunov 指数。我们的数据表明，安德森模型表现出比迄今已确立的更为丰富的行为。
