论文标题
Wigner矩阵的特征态热假说
Eigenstate Thermalization Hypothesis for Wigner Matrices
论文作者
论文摘要
我们证明，任何确定性矩阵都大致是大型随机Wigner矩阵的本本bas中的身份，其概率很高，并且与维度的平方根成反比最佳误差。因此，我们的定理严格验证了Deutsch [Deutsch 1991]的特征态热假说，以最简单的混沌量子系统，即Wigner Ensemble。用数学术语，我们同时证明了所有特征向量的量子独特型（QUE）的强烈形式，并具有最佳的收敛速率，从而概括了先前的概率que，导致[Bourgade，Yau，Yau 2017]和[Bourgade，Yau，Yau，Yau，Yau，Yin 2020]。
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalization Hypothesis by Deutsch [Deutsch 1991] for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in [Bourgade, Yau 2017] and [Bourgade, Yau, Yin 2020].
