零温有隙系统的Kubo公式证明：简要综述与若干新结果
Justifying Kubo's formula for gapped systems at zero temperature: a brief review and some new results
AI总结：
本文综述零温有隙量子系统Kubo公式的严格证明问题及与量子霍尔效应的关联，介绍基于NEASS和绝热定理的线性响应方法，并将有限格点结果通过热力学极限推广到无限系统。
摘要：
我们首先综述了零温下有隙扩展哈密顿量子系统中输运系数的Kubo公式的严格证明问题。具体而言，量子霍尔效应的理论理解依赖于这类系统中Kubo公式的有效性，我们也简要回顾了这一关联。随后我们重点介绍了一种基于非平衡近稳态（NEASS）及相应绝热定理的线性响应理论方法，该方法由我们中的一位学者近期在文献[51]中针对有限格点上的相互作用费米子系统提出并推导完成。在论文的第二部分，我们展示了如何通过取热力学极限，将文献[51]的结果推广至无限系统。
英文摘要：
We first review the problem of a rigorous justification of Kubo's formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo's formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
