The optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo's linear response theory, we study the general properties of the nonlinear optical conductivities of quantum many-body systems both in equilibrium and non-equilibrium. We discuss a generalization of the $f$-sum rule to a non-equilibrium setting by focusing on the instantaneous response. Furthermore, we obtain an expression of the second- and the third-order optical conductivity in terms of correlation functions and present a perturbative proof of the generalized Kohn formula proposed recently.

中文翻译：

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关于非线性光导率的一般性质

光导率是材料的基本定义特性，表征电流对时间相关电场的响应。在这项工作中，我们遵循 Kubo 线性响应理论的方法，研究了平衡和非平衡量子多体系统非线性光导率的一般性质。我们通过关注瞬时响应来讨论 $f$-sum 规则对非平衡设置的推广。此外，我们根据相关函数获得了二阶和三阶光导率的表达式，并提供了最近提出的广义 Kohn 公式的微扰证明。