AI 中文总结
研究一般Rosenzweig-Porter型模型的本征向量局域化性质和本征态热化假说，统一处理任意厄米矩阵H0与耦合常数λ，证明迁移率边和重入局域化现象。
AI 中文摘要
我们考虑一个非常一般的Rosenzweig-Porter型模型，$H=H_0+\lambda W$，其中$H_0$是任意厄米矩阵，$W$是标准Wigner矩阵。我们精确追踪了当耦合常数$\lambda$在平凡的$\lambda=0$情形和完全平均场的大$\lambda$区域之间插值时，本征向量的局域化性质和本征态热化假说（ETH）。我们的结果对$H_0$和$\lambda$一致成立，实质上推广了所有先前关于变形Wigner矩阵的局部定律，即使在平均场区域也是如此。我们的证明精确捕捉了预解式的确定性近似，该近似表现出强烈非均匀结构。作为副产品，我们得出了迁移率边的出现并研究了重入局域化现象。
英文摘要
We consider a very general Rosenzweig-Porter-type model, $H=H_0+λW$, where $H_0$ is an arbitrary Hermitian matrix and $W$ is a standard Wigner matrix. We precisely trace the localization properties of the eigenvectors and the eigenstate thermalisation hypothesis (ETH) as the coupling constant $λ$ interpolates between the trivial $λ=0$ case and the fully mean field regime of large $λ$. Our results hold uniformly in $H_0$ and $λ$, substantially generalising all previous local laws on deformed Wigner matrices even in the mean field regime. Our proof precisely captures the deterministic approximation to the resolvent which exhibits a strongly inhomogeneous structure. As a byproduct, we conclude the emergence of a mobility edge and study the phenomenon of re-entrant localization.
Comments55 pages, 3 figures; v1 -> v2: minor update, added references
