一维安德森局域化：统计异常的魔鬼阶梯
One-dimensional Anderson Localization: Devil's staircase of Statistical Anomalies
摘要：
考虑了一维Anderson局域化模型中波函数的统计特性。它表明，在任何能量，对应于一个合理的填充因子f=p/q有一个统计异常，这是看到在扩展的生成函数（GF）的顺序（q-2）的无序参数。我们详细研究了在$f=1/2$的主要异常出现在领先的顺序。本文导出了具有二维内部空间的Fokker-Planck型转移矩阵方程。结果表明，该方程的零模变量是可积的，并在热力学极限下找到了生成函数的解。
英文摘要：
The statistics of wavefunctions in the one-dimensional (1d) Anderson model of localization is considered. It is shown that at any energy that corresponds to a rational filling factor f=p/q there is a statistical anomaly which is seen in expansion of the generating function (GF) to the order (q-2) in the disorder parameter. We study in detail the principle anomaly at $f=1/2$ that appears in the leading order. The transfer-matrix equation of the Fokker-Planck type with a two-dimensional internal space is derived for GF. It is shown that the zero-mode variant of this equation is integrable and a solution for the generating function is found in the thermodynamic limit.
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