一维随机介质单参数标度的微扰检验
Perturbative test of single parameter scaling for 1D random media
摘要：
与一维随机介质相关的随机矩阵的乘积满足中心极限定理，该定理确保收敛到以李雅普诺夫指数为中心的高斯。单参数标度假设表明其方差等于李雅普诺夫指数。我们解决讨论其有效性的广泛的一类模型证明，远离异常，单参数标度举行最低阶扰动理论的无序强度。然而，它一般是违反了更高的秩序。这一点在安德森模型中得到了明确的体现。
英文摘要：
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single parameter scaling holds to lowest order perturbation theory in the disorder strength. However, it is generically violated at higher order. This is explicitely exhibited for the Anderson model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
