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摘要翻译：
对于无序紧束缚晶格模型（Anderson模型）和某些随机矩阵系综，我们考虑重合点处两个单粒子概率密度$\psi_{E}（{bf r}）^{2}$的相关性作为能量分离$\omega=e-e′$的函数。我们重点讨论了参数范围内的模型，在这些参数范围内它们是接近的，但并不完全处于Anderson局部化转变。我们发现，即使远离临界点，本征函数关联也表现出临界状态特征的多重分形残余。结合Anderson模型的数值结果和相关随机矩阵理论的解析和数值结果，我们能够识别出描述金属和绝缘体相中多重分形特征的高斯随机矩阵系综。特别地，这些随机矩阵系综描述了我们在Anderson模型上模拟发现的本征函数相关的新现象。在二维和三维Anderson绝缘体中，大能量分离时本征函数相互回避，小能量分离时本征函数关联的对数增强。对这两种现象都提出了一个简单而普遍的物理图景。
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英文标题：
《Two-eigenfunction correlation in a multifractal metal and insulator》
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作者：
E. Cuevas and V. E. Kravtsov
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Mesoscale and Nanoscale Physics 介观和纳米物理
分类描述：Semiconducting nanostructures: quantum dots, wires, and wells. Single electronics, spintronics, 2d electron gases, quantum Hall effect, nanotubes, graphene, plasmonic nanostructures
半导体纳米结构：量子点、线和阱。单电子学，自旋电子学，二维电子气，量子霍尔效应，纳米管，石墨烯，等离子纳米结构
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We consider the correlation of two single-particle probability densities $|\Psi_{E}({\bf r})|^{2}$ at coinciding points ${\bf r}$ as a function of the energy separation $\omega=|E-E'|$ for disordered tight-binding lattice models (the Anderson models) and certain random matrix ensembles. We focus on the models in the parameter range where they are close but not exactly at the Anderson localization transition. We show that even far away from the critical point the eigenfunction correlation show the remnant of multifractality which is characteristic of the critical states. By a combination of the numerical results on the Anderson model and analytical and numerical results for the relevant random matrix theories we were able to identify the Gaussian random matrix ensembles that describe the multifractal features in the metal and insulator phases. In particular those random matrix ensembles describe new phenomena of eigenfunction correlation we discovered from simulations on the Anderson model. These are the eigenfunction mutual avoiding at large energy separations and the logarithmic enhancement of eigenfunction correlations at small energy separations in the two-dimensional (2D) and the three-dimensional (3D) Anderson insulator. For both phenomena a simple and general physical picture is suggested.
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PDF链接：
https://arxiv.org/pdf/707.4585
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