Scaling studies of the resistance of the one-dimensional Anderson model with general disorder
Scaling studies of the resistance of the one-dimensional Anderson model with general disorder
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一维安德森模型对一般疾病的抵抗力的标度研究
DOI：
10.1103/physrevb.24.5583
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发表时间：
1981
影响因子：
3.7
通讯作者：
D. Chadi
中科院分区：
文献类型：
--
作者：
A. Stone;J. Joannopoulos;D. Chadi
用解析和数值方法研究了同时具有对角无序和非对角无序的一维安德森模型的电阻ρ。发展了一种递推方法，并用它导出了任意无序E=0时平均电阻和弱无序极限下E≠0的精确标度律.在所有情况下，平均电阻都随着样本的长度L呈指数增长。我们还发现典型的电阻ρ̃=exp[<；ln(1+ρ)>；]−1在所有情况下都与L指数增长，除了纯非对角无序在E=0处，这里<；ln(1+ρ)>；∝L给出了这个特例的存在的解释，表明我们所有的结果都符合ρ>；>；1的电阻的对数正态概率分布。对数值平均的可靠性进行了定量的估计，表明数值平均值只会非常缓慢地收敛到解析结果。这定性地解释了L在几次数值计算中发现的ln<；ρ>；慢于线性增长的现象，并探讨了它对实验的影响。
The resistance ρ of a one-dimensional Anderson model with both diagonal and off-diagonal disorder is studied by analytic and numerical techniques. A recursive method is developed and used to derive an exact scaling law for the average resistance at E= 0 for arbitrary disorder, and for E≠ 0 in the limit of weak disorder. The average resistance grows exponentially with L, the length of the sample, in all cases. The typical resistance ρ ̃= exp [< ln (1+ ρ)>]− 1 is also found to grow exponentially with L in all cases, except for purely off-diagonal disorder at E= 0, where< ln (1+ ρ)>∝ L. An explanation is given for the existence of this special case and it is shown that all our results are consistent with a lognormal probability distribution of the resistance for ρ>> 1. Quantitative estimates are made of the reliability of numerically performed averages which show that a numerical average will converge only very slowly to the analytic result. This provides a qualitative explanation of the slower than linear growth of ln< ρ> with L found in several numerical calculations; its consequences for experiment are also explored.