In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green’s function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.

在本文中，我们首先试图阐明文献中在将标准线性响应理论 (LRT) 概括为海森堡图片中的开放量子系统理论时存在的歧义，该理论基本上是为封闭系统制定的。然后，我们使用所谓的广义 LRT 研究了驱动耗散光机械系统 (OMS) 对弱时间相关扰动的线性响应。它显示了如何从海森堡图片中的量子朗之万方程 (QLE) 中获得作为开放量子系统的标准 OMS 运动的格林函数方程。获得的结果解释了大量现象，包括反共振、正常模式分裂和光机械诱导透明度（OMIT）。此外，