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.

中文翻译：

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证明 Kubo 的零温度间隙系统公式的合理性：简要回顾和一些新结果

我们首先回顾了 Kubo 的零温度下间隙扩展哈密顿量子系统中的传输系数公式的严格证明问题。特别是，对量子霍尔效应的理论理解依赖于久保公式对此类系统的有效性，我们也简要回顾了这一联系。然后，我们强调了一种基于非平衡几乎稳态 (NEASS) 的线性响应理论方法，以及我们最近在 [51] 中提出并制定的此类系统的相应绝热定理，用于在有限格。在我们论文的第二部分，我们展示了如何通过热力学极限将 [51] 的结果提升到无限系统。