论文标题
特征态热假说中对角线和外对角功能的半经典研究
Semiclassical study of diagonal and offdiagonal functions in the eigenstate thermalization hypothesis
论文作者
论文摘要
所谓的特征态热假说（ETH）已通过数值模拟在许多体育模型中进行了测试，它提供了一种理解最终热化的方法，并且认为对于理解热化过程非常重要。两个功能在ETH的应用中起着重要作用，一个功能在平均对角线元素中起着重要作用，另一个功能在ETH在能量基础上可观察到的offiagonal元素的差异。对于以前的函数，已知的HBAR零序是半经典表达的，而后者在分析上几乎不知道。在本文中，为前者函数得出了半经典表达式，其中包括HBAR的高阶贡献。并且，在动作基础上，能量本征征的相关性可忽略不计，因此为后一种函数得出了半经典近似。分析预测的相关性在Lipkin-Meshkov-Glick模型中进行数值测试。
The so-called eigenstate thermalization hypothesis (ETH), which has been tested in various manybody models by numerical simulations, supplies a way of understanding eventual thermalization and is believed to be important for understanding processes of thermalization. Two functions play important roles in the application of ETH, one for averaged diagonal elements and the other for the variance of offdiagonal elements of an observable addressed by ETH on the energy basis. For the former function, a semiclassical expression is known of the zeroth order of hbar, while, little is known analytically for the latter. In this paper, a semiclassical expression is derived for the former function, which includes higher-order contributions of hbar. And, a semiclassical approximation is derived for the latter function, under the assumption of negligible correlations among energy eigenfuntions on an action basis. Relevance of the analytical predictions are tested numerically in the Lipkin-Meshkov-Glick model.
