From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective
From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective
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从非遍历特征向量到局部解析统计并返回：随机矩阵视角
DOI：
10.1209/0295-5075/115/47003
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
G. Biroli
中科院分区：
文献类型：
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作者：
Davide Facoetti;P. Vivo;G. Biroli
我们研究了广义Rosenzweig-Porter随机矩阵模型的特征向量的局部预解式和非遍历性质的统计，经历了两个由离域非遍历相分离的过渡。将该模型解释为原位随机能量和结构无序跳跃的组合，我们发现每个本征态在能量接近的位点上离域，与Kravtsov等人（New J. Phys.，17（2015）122002）。我们的其他主要结果，得到的递归关系相结合的预解矩阵的见解戴森的布朗运动，是显示的非遍历离域相的属性可以探讨研究统计的本地预解在一个非标准的缩放限制。
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies and a structurally disordered hopping, we found that each eigenstate is delocalised over sites close in energy in agreement with Kravtsov et al. (New J. Phys., 17 (2015) 122002). Our other main result, obtained combining a recurrence relation for the resolvent matrix with insights from Dyson's Brownian motion, is to show that the properties of the non-ergodic delocalised phase can be probed studying the statistics of the local resolvent in a non-standard scaling limit.