树图上Anderson模型的大连通极限
The Large Connectivity Limit of the Anderson Model on Tree Graphs
摘要：
我们考虑无限正则树上的Anderson局部化问题。在本地化阶段，我们得到了严格的下界的自由能函数最近推出的Aizenman和Warzel。使用有限体积正则化，我们还得到了这个自由能函数的上界。这就产生了临界无序的上界和下界，使得给定能量下的所有状态都变得局域化。这些界限在它们匹配的大连通性极限中特别有用，证实了Abou-Chacra，Anderson和Wavelless的早期预测。
英文摘要：
We consider the Anderson localization problem on the infinite regular tree. Within the localized phase, we derive a rigorous lower bound on the free energy function recently introduced by Aizenman and Warzel. Using a finite volume regularization, we also derive an upper bound on this free energy function. This yields upper and lower bounds on the critical disorder such that all states at a given energy become localized. These bounds are particularly useful in the large connectivity limit where they match, confirming the early predictions of Abou-Chacra, Anderson and Thouless.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
