ABSTRACT

Resistance ρ of an one-dimensional disordered system of length L has the log-normal distribution in the limit of large L. Parameters of this distribution depend on the Fermi level position, but are independent on the boundary conditions. However, the boundary conditions essentially affect the distribution of phases entering the transfer matrix and generally change the parameters of the evolution equation for the distribution $P\left(\rho \right)$. This visible contradiction is resolved by the existence of the hidden symmetry, whose nature is revealed by the derivation of the equation for the stationary phase distribution and by analysis of its transformation properties.

中文翻译：

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一维定位中的隐藏对称性

摘要

长度为L的一维无序系统的电阻ρ在大L的极限内呈对数正态分布。此分布的参数取决于费米能级位置，但与边界条件无关。然而，边界条件本质上会影响进入传递矩阵的相的分布，并且通常会改变分布的演化方程的参数$磷\left(\rho \right)$. 这种可见的矛盾通过存在隐藏的对称性来解决，其性质通过对固定相分布方程的推导和对其变换特性的分析来揭示。