论文标题
在接近经典限制的特征态热缩放
Eigenstate thermalization scaling in approaching the classical limit
论文作者
论文摘要
根据本征态热假说（ETH），局部可观察物的期望值的本征态到元素的波动应随着系统大小的增加而降低。在接近热力学限制时 - 地点数量和以相同速率增加的粒子数 - 波动应扩展为Hilbert Space Dimension $ d $的$ \ sim d^{ - 1/2} $。在这里，我们通过增加固定晶格拓扑中的颗粒数来研究不同的极限 - 经典或半经典的极限。我们专注于范式的Bose-Hubbard系统，该系统对于大晶格来说是量子 - 偶然的，并且显示出小晶格的混合行为。假设具有高斯分布的随机组件的理想特征状态，我们会得出预期缩放的表达式。我们从数字上表明，对于较大的晶格，物理中谱特征状态的ETH缩放遵循理想（高斯）期望，但是对于较小的晶格，缩放是通过不同的指数进行的。我们检查了这种异常缩放的几种合理机制。
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.
