Multifractality and statistical localization in highly heterogeneous random networks

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

EPL Pub Date : 2023-11-27 DOI:10.1209/0295-5075/ad1001

Diego Tapias, Peter Sollich

引用次数: 0

Abstract We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk. We study the structure of the eigenvectors associated with this divergence and find that they are multifractal with the statistics of eigenvector elements matching those of the resolvent entries. The corresponding localization mechanism relies on the statistical properties of the nodes rather than on any spatial structure around a localization centre. This “statistical localization” mechanism is potentially relevant for explaining localization in different models that display singularities in the bulk of the spectrum of eigenvalues.

查看原文本刊更多论文

高度异构随机网络中的多分形和统计定位

摘要我们考虑了在高连通性极限下具有对称相互作用的高度异构随机网络。该系统的一个主要特征是，相应集合的谱密度在主体内呈现发散。我们研究了与这种发散相关的特征向量结构，发现它们是多分形的，特征向量元素的统计量与解析项的统计量相匹配。相应的定位机制依赖于节点的统计特性，而不是定位中心周围的任何空间结构。这种 "统计定位 "机制可能与解释不同模型中的定位相关，这些模型在特征值谱的大部分显示奇异性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

EPL 物理-物理：综合

CiteScore

3.30

自引率

5.60%

发文量

332

审稿时长

1.9 months

期刊介绍： General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.