Murphy N Benjamin, Cherkaev Elena, Golden Kenneth M
Department of Mathematics, University of Utah, 155 S 1400 E RM 233, Salt Lake City, Utah 84112-0090, USA.
Phys Rev Lett. 2017 Jan 20;118(3):036401. doi: 10.1103/PhysRevLett.118.036401. Epub 2017 Jan 19.
The Anderson transition in solids and optics is a wave phenomenon where disorder induces localization of the wave functions. We find here that the hallmarks of the Anderson transition are exhibited by classical transport at a percolation threshold-without wave interference or scattering effects. As long range order or connectedness develops, the eigenvalue statistics of a key random matrix governing transport cross over toward universal statistics of the Gaussian orthogonal ensemble, and the field eigenvectors delocalize. The transition is examined in resistor networks, human bone, and sea ice structures.
固体和光学中的安德森转变是一种波动现象，其中无序会导致波函数的局域化。我们在此发现，安德森转变的特征在渗流阈值处的经典输运中表现出来，而不存在波干涉或散射效应。随着长程有序或连通性的发展，控制输运的关键随机矩阵的本征值统计向高斯正交系综的通用统计转变，并且场本征向量离域化。在电阻网络、人体骨骼和海冰结构中对这种转变进行了研究。
