The generalized DMPK equation revisited: towards a systematic derivation
The generalized DMPK equation revisited: towards a systematic derivation
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DOI：
10.1088/1751-8113/47/12/125103
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
A. Douglas;P. Markoš;K. Muttalib
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文献类型：
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作者：
A. Douglas;P. Markoš;K. Muttalib
广义Dorokov-Mello-Pereyra-Kumar（DMPK）方程最近被用来获得三维无序导体的一系列非常广泛和高度不对称的电导分布。然而，对广义DMPK方程的推导有两个主要的批评：（1）某些本征向量相关性被忽略，这是基于定性的论点，不能对所有无序强度都有效，（2）两个紧密间隔的本征值之间的排斥并不严格受对称性考虑的影响。在这项工作中，我们表明，它是可以解决这两个批评，包括本征值和本征向量的相关性在一个系统和控制的方式。事实证明，添加的相关性确定雅可比矩阵的演变，而不影响电导分布的评估。它们还保证了对称性要求。此外，我们得到了一个确切的特征向量和Lyapunov指数之间的关系，导致后者在所有的无序强度的总和规则。
The generalized Dorokov–Mello–Pereyra–Kumar (DMPK) equation has recently been used to obtain a family of very broad and highly asymmetric conductance distributions for three-dimensional disordered conductors. However, there are two major criticisms of the derivation of the generalized DMPK equation: (1) certain eigenvector correlations were neglected based on qualitative arguments that cannot be valid for all strengths of disorder, and (2) the repulsion between two closely spaced eigenvalues were not rigorously governed by symmetry considerations. In this work we show that it is possible to address both criticisms by including the eigenvalue and eigenvector correlations in a systematic and controlled way. It turns out that the added correlations determine the evolution of the Jacobian, without affecting the evaluation of the conductance distributions. They also guarantee the symmetry requirements. In addition, we obtain an exact relationship between the eigenvectors and the Lyapunov exponents leading to a sum rule for the latter at all disorder strengths.