Kubo’s linear response theory is a general theory on the susceptibility or magnetization of the medium and various transport phenomena in the equilibrium region. It is based on the first-order perturbation theory and has been extended from single system to composite system in recent years. They most care about the response of the whole system but barely explore for the subsystem’s response of the composite system. In this paper, we develop a linear response theory for composite system to gain the subsystem’s information. We formulate this theory in terms of general susceptibility, after which we apply it to the derivation of a time-independent composite system composed of two coupled subsystems. That is calculating the response of subsystem 2 caused by the subsystem 1 subjected to perturbation. For a better explanation, we examine the susceptibility’s (imaginary part) images with various parameters. We point out the imaginary part of the susceptibility can be represented by Dirac δ function and change with temperature and the coupling strength. Our results provide a promising platform for the coherent manipulation of the linear response in composite system, which has potential applications for quantum information processing and statistical physics.

中文翻译：

---

复合系统的线性响应理论

久保的线性响应理论是关于平衡区域内介质的磁化率或磁化强度以及各种输运现象的一般理论。它基于一阶微扰理论，近年来从单一系统扩展到复合系统。他们最关心的是整个系统的响应，而很少探索子系统对复合系统的响应。在本文中，我们开发了复合系统的线性响应理论来获取子系统的信息。我们根据一般敏感性来阐述这个理论，然后我们将其应用于由两个耦合子系统组成的时间无关复合系统的推导。即计算子系统 1 受到扰动引起的子系统 2 的响应。为了更好的解释，我们检查具有各种参数的磁化率（虚部）图像。我们指出磁化率的虚部可以用狄拉克δ函数表示，并随温度和耦合强度而变化。我们的结果为复合系统中线性响应的相干操纵提供了一个有前途的平台，该平台在量子信息处理和统计物理方面具有潜在的应用。