标题： 本征态热化在接近经典极限时的标度行为 显示英文标题

标题： Eigenstate thermalization scaling in approaching the classical limit

摘要： 根据本征态热化假说（ETH），局部可观测量的本征态到本征态的期望值波动应随着系统尺寸的增加而减小。 在接近热力学极限——即格点数和粒子数以相同速率增加——的情况下，波动应按照$\sim D^{-1/2}$与希尔伯特空间维度$D$的关系进行缩放。 在这里，我们研究另一种极限——经典或半经典极限——通过在固定晶格拓扑中增加粒子数来实现。 我们关注典型的玻色-哈伯德系统，在大晶格中它是量子混沌的，在小晶格中表现出混合行为。 我们推导了预期缩放的表达式，假设理想本征态具有高斯分布的随机分量。 我们数值证明，对于较大的晶格，物理中间谱本征态的ETH缩放符合理想的（高斯）期望，但对于较小的晶格，缩放通过不同的指数发生。 我们检查了几种可能的机制来解释这种异常缩放。 显示英文摘要

摘要： According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit - the number of sites and the particle number increasing at the same rate - the fluctuations should scale as $\sim D^{-1/2}$ with the Hilbert space dimension $D$. Here, we study a different limit - the classical or semiclassical limit - by increasing the particle number in fixed lattice topologies. We focus on the paradigmatic Bose-Hubbard system, which is quantum-chaotic for large lattices and shows mixed behavior for small lattices. We derive expressions for the expected scaling, assuming ideal eigenstates having Gaussian-distributed random components. We show numerically that, for larger lattices, ETH scaling of physical mid-spectrum eigenstates follows the ideal (Gaussian) expectation, but for smaller lattices, the scaling occurs via a different exponent. We examine several plausible mechanisms for this anomalous scaling.