Exactly solvable model with two conductor-insulator transitions driven by impurities
Exactly solvable model with two conductor-insulator transitions driven by impurities
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DOI：
10.1103/physrevlett.86.2621
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发表时间：
2001-03-19
影响因子：
8.6
通讯作者：
Golinelli, O
中科院分区：
文献类型：
--
作者：
Bauer, M;Golinelli, O
我们对随机图模型中的两个导体-绝缘体转变进行了精确分析，其中低连通性意味着高杂质浓度。随机图的邻接矩阵用作跳跃哈密顿量。我们准确地计算了光谱中零能量处的δ峰的高度，并分析地描述了局部特征向量的结构和贡献。对于 1.421 529... 和 3.154 985... 之间的平均连通性，该系统是导体，但在其他情况下是绝缘体。我们解释了平均连通性 e = 2.718 281... 处的谱奇异性，并将其与随机图论中的其他枚举问题联系起来。
We present an exact analysis of two conductor-insulator transitions in the random graph model where low connectivity means high impurity concentration. The adjacency matrix of the random graph is used as a hopping Hamiltonian. We compute the height of the delta peak at zero energy in its spectrum exactly and describe analytically the structure and contribution of localized eigenvectors. The system is a conductor for average connectivities between 1.421 529... and 3.154 985... but an insulator in the other regimes. We explain the spectral singularity at average connectivity e = 2.718 281... and relate it to other enumerative problems in random graph theory.