论文标题
隔离量子系统的波动耗散定理的数值验证
Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
论文作者
论文摘要
波动耗散定理（FDT）是吉布斯状态中热平衡系统的标志。我们解决了一个问题，即在能量本特征中，孤立的量子系统是否遵守FDT。在本征态热假说的框架中，我们得出了在能量本征态或对角线集合中两次相关函数的形式表达。他们满足了在无限的系统尺寸限制下的Kubo-Martin-Schwinger条件，这是FDT的足够和必要条件。我们还获得了有限大小系统的FDT的有限尺寸校正。借助XXZ自旋链模型的大量数值作品，我们确认了FDT和有限尺寸校正的理论。我们的结果可以用作有限大小系统中FDT的实验研究的指南。
The fluctuation dissipation theorem~(FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.
