AI 中文总结
针对具有柯西无序的贝特格点的安德森局域化问题，提出典型介质理论的数值与解析结合方案，推导典型态密度的解析表达式，得到简化自洽方案，揭示迁移边连续坍缩及扩展态消失的规律。
AI 中文摘要
我们针对无限连接的贝特格点上具有柯西分布在位无序的安德森局域化问题，提出了典型介质理论（TMT）的数值与解析可处理的结合实现方案。利用柯西分布与贝特格点的特殊性质，我们推导了典型态密度（TDOS）的解析表达式，并得到了简化的TMT自洽方案。研究表明，带中心处的TDOS随无序强度线性减小，且在临界无序强度W_c=D/2时消失；所得ω-W相图揭示了迁移边的连续坍缩以及扩展态的消失。
英文摘要
We present a combined numerical and analytically tractable realization of the typical medium theory (TMT) for Anderson localization on the infinite-connectivity Bethe lattice with Cauchy-distributed on-site disorder. Exploiting the special properties of the Cauchy distribution and the Bethe lattice, we derive an analytical expression for the typical density of states (TDOS) and obtain a simplified TMT self-consistency scheme. We show that the TDOS at the band center decreases linearly with disorder strength and vanishes at the critical disorder $W_c=D/2$. The resulting $ω$--$W$ phase diagram reveals the continuous collapse of the mobility edge and the disappearance of extended states.
Comments12 pages, 7 figures
