论文标题
Miller-Abrahams随机电阻网络，Mott Random Walk和2级均质化
Miller-Abrahams random resistor network, Mott random walk and 2-scale homogenization
论文作者
论文摘要
Miller-Abrahams（MA）随机电阻网络由一个完整的图形在具有边缘电导率的标记简单过程上的完整图给出，具体取决于标记，并在边缘长度上呈指数衰减。作为Mott Random Walk，它是研究Mott可变范围在无定形固体中作为掺杂的半导体跳跃的有效模型。通过使用2级均质化，我们证明了A.S. MA电阻网络的无限量电导率由有效的均质矩阵$ d $给出。此外，$ d $承认了变异表征，并等于莫特随机步行的限制扩散矩阵。该结果阐明了这两种模型之间的关系，并且还允许将$ d $与物理莫特法律一致的现有界限扩展到MA电阻网络[12,14]。后一种涉及低温拉伸的无定形固体电导率衰减。此处开发的技术可以应用于其他模型，例如随机电导模型[11]，没有椭圆度假设。
The Miller-Abrahams (MA) random resistor network is given by a complete graph on a marked simple point process with edge conductivities depending on the marks and decaying exponentially in the edge length. As Mott random walk, it is an effective model to study Mott variable range hopping in amorphous solids as doped semiconductors. By using 2-scale homogenization we prove that a.s. the infinite volume conductivity of the MA resistor network is given by an effective homogenized matrix $D$. Moreover $D$ admits a variational characterization and equals the limiting diffusion matrix of Mott random walk. This result clarifies the relation between the two models and it also allows to extend to the MA resistor network the existing bounds on $D$ in agreement with the physical Mott law [12,14]. The latter concerns the low temperature stretched exponential decay of conductivity in amorphous solids. The techniques developed here can be applied to other models, as e.g. the random conductance model [11], without ellipticity assumptions.
