摘要翻译：
我们研究了磁场存在下无限长矩形量子图的光谱性质。我们研究了当考虑三维特性时，这些特性是如何受到影响的，特别是流变特性。然后我们建立了这些系统的霍尔横向电导率的量子化。这种量子化是通过将横向电导率与拓扑不变量联系起来得到的。对于各向异性扩散系统，显式地计算了霍尔电导率的不同整数值，得到了分形相图。
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英文标题：
《Quantum graphs and the integer quantum Hall effect》
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作者：
N. Goldman and P. Gaspard
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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 study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establish the quantization of the Hall transverse conductivity for these systems. This quantization is obtained by relating the transverse conductivity to topological invariants. The different integer values of the Hall conductivity are explicitly computed for an anisotropic diffusion system which leads to fractal phase diagrams.
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PDF链接：
https://arxiv.org/pdf/709.1567