二维量子渗流模型中的局域-离域跃迁

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摘要翻译：
研究了二维随机稀释渗流团簇中量子粒子在正方形和三角形晶格上的跳跃输运。我们通过计算透射系数作为能量的函数(-2<E<2，在紧束缚哈密顿量中，以跳跃积分为单位）和无序度q（给定晶格位置对粒子不可用的概率）来研究粒子局域化的性质。我们基于有限尺寸标度的研究表明，离域态的存在依赖于系统中存在的能量和无序量。对于远离能带中心的能量(E=0)，只有在低无序(q<15%)时才出现离域态。对于任何数量的无序，带中心附近的传输通常都很小，因此很难定位到离域态的跃迁，但我们的研究确实表明了一种比幂律局域化更弱的行为。除了这种局域-离域转变，我们还发现了两种不同的局域状态的存在，这取决于能量和无序量。对于给定的能量，对于足够高的无序度，态是指数局域的。随着无序度的减小，态首先表现为幂律局域化，然后才表现为非局域化行为。
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英文标题：
《Localization-delocalization transition in 2D quantum percolation model》
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作者：
Md Fhokrul Islam, Hisao Nakanishi
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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：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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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 hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by calculating the transmission coefficient as a function of energy (-2 < E < 2 in units of the hopping integral in the tight-binding Hamiltonian) and disorder, q (probability that a given site of the lattice is not available to the particle). Our study based on finite size scaling suggests the existence of delocalized states that depends on energy and amount of disorder present in the system. For energies away from the band center (E = 0), delocalized states appear only at low disorder (q < 15%). The transmission near the band center is generally very small for any amount of disorder and therefore makes it difficult to locate the transition to delocalized states if any, but our study does indicate a behavior that is weaker than power-law localization. Apart from this localization-delocalization transition, we also find the existence of two different kinds of localization regimes depending on energy and amount of disorder. For a given energy, states are exponentially localized for sufficiently high disorder. As the disorder decreases, states first show power-law localization before showing a delocalized behavior.
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PDF链接：
https://arxiv.org/pdf/709.4085

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关键词：三角形 正方形 幂律 percolation 中心 amount two