一维高斯关联势中的广义李雅普诺夫指数和透射统计
Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials
摘要：
利用广义李雅普诺夫指数（LE）和lnT的累积量，对具有关联高斯无序的长系统的透射系数T的分布进行了解析和数值研究.在弱无序、中等无序和强无序下，考虑了不同的无序关联模型对这些量的影响。得到了lnT的累积量之间的标度关系。在强无序的半经典近似内的累积量的处理解析，和数值任意强度的障碍。本文提出了一种计算一般关联无序广义LE的小关联尺度近似。发现了无序关联对传输统计的重要影响，特别是累积量之间的关系以及累积量与广义LE之间的关系表明，在弱无序之外，由于无序关联，传输涨落及其分布偏离对数正态形式（在长而有限的系统中）的程度大大增强。这些影响的相关尺度的参数依赖。
英文摘要：
Distribution of the transmission coefficient T of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect of the disorder correlations on these quantities is considered in weak, moderate and strong disorder for different models of correlation. Scaling relations between the cumulants of lnT are obtained. The cumulants are treated analytically within the semiclassical approximation in strong disorder, and numerically for an arbitrary strength of the disorder. A small correlation scale approximation is developed for calculation of the generalized LE in a general correlated disorder. An essential effect of the disorder correlations on the transmission statistics is found. In particular, obtained relations between the cumulants and between them and the generalized LE show that, beyond weak disorder, transmission fluctuations and deviation of their distribution from the log-normal form (in a long but finite system) are greatly enhanced due to the disorder correlations. Parametric dependence of these effects upon the correlation scale is presented.
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