AI 中文总结
证明大N×N平均场随机矩阵的本征态热化假设（ETH），确定微正则系综及本征向量重叠的最优涨落尺度，揭示依赖多预解式局部定律的机制，发现正则谱边缘涨落速率的异常。
AI 中文摘要
我们证明了具有一般相关结构的大N×N平均场随机矩阵的本征态热化假设（ETH），也称为量子唯一遍历性（QUE）。我们确定了微正则系综，并建立了围绕它的本征向量重叠的最优涨落尺度。我们的结果推翻了Feingold和Peres在量子混沌物理文献中的预测，并揭示了依赖多预解式局部定律的真正机制。
英文摘要
We prove the Eigenstate Thermalisation Hypothesis (ETH), also known as Quantum Unique Ergodicity (QUE), for large $N\times N$ mean-field random matrices with general correlation structure. We identify the microcanonical ensemble and establish the optimal fluctuation scale of eigenvector overlaps around it. Our results invalidate the inverse-density scaling predicted by Feingold and Peres [Phys. Rev. A 34, 591 (1986)] (and incorporated into Srednicki's ansatz [Phys. Rev. E 50, 888-901 (1994)]) in the physics literature of quantum chaos, based upon popular semiclassical theory, and uncover the genuine mechanism which relies on multi-resolvent local laws. Although fluctuations are expected to increase as the density of states vanishes, and indeed scale as $N^{-1/2}$ in the special cusp regime, rather than $N^{-1}$ in the bulk, we find, unexpectedly, that the same $N^{-1}$ rate persists at regular spectral edges. Hence, generically, in the absence of cusps, the entire eigenbasis fluctuates on the same scale as a Haar unitary. This anomaly stems from delicate cancellations in the solution of the underlying matrix Dyson equation, which form the core of our analysis.
Comments116 pages, 3 figures, 2 tables
