论文标题
稀疏Barrat-Mézard陷阱模型的本地化特性
Localization properties of the sparse Barrat-Mézard trap model
论文作者
论文摘要
受稀疏图上安德森模型的作品的启发，我们设计了一种方法来分析稀疏系统的本地化特性，可以使用腔理论解决。我们应用这种方法来研究稀疏Barrat-Mézard陷阱模型的总操作员特征向量的特性，并重点是扩展相。作为定位的探针，我们考虑了反向参与率和相关量，都取决于分解的对角线元素的分布。我们的结果揭示了估计量跨松弛率范围的丰富和非平凡行为，以及熵和激活机制之间的相互作用，从而导致嵌入在大部分扩展状态中的局部模式。我们表征了这种定位途径，并发现它与范式的Anderson模型或标准随机矩阵系统不同。
Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze the localization properties of sparse systems that may be solved using cavity theory. We apply this method to study the properties of the eigenvectors of the master operator of the sparse Barrat-Mézard trap model, with an emphasis on the extended phase. As probes for localization, we consider the inverse participation ratio and the correlation volume, both dependent on the distribution of the diagonal elements of the resolvent. Our results reveal a rich and non-trivial behavior of the estimators across the spectrum of relaxation rates and an interplay between entropic and activation mechanisms of relaxation that give rise to localized modes embedded in the bulk of extended states. We characterize this route to localization and find it to be distinct from the paradigmatic Anderson model or standard random matrix systems.
