Theory of a General Quantum System Interacting with a Linear Dissipation System

Richard P. Feynman, Frank L. Vernon

R. P. Feynman

Richard P. Feynman, F.L Vernon

Ilya Prigogine

Behrouz Askari, Ali Dalafi

Abstract In this article, the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Bose–Einstein condensate to an external time-dependent perturbation is studied in the framework of the generalized linear response theory (GLRT). It is shown that the Stokes and anti-Stokes amplitudes of the optical and atomic modes of the system can be obtained through the solutions to the equations of motion of the open quantum system Green’s function predicted by the GLRT. In this way, interesting phenomena like anti-resonance and Fano resonance are described and it is shown how the atom–atom interaction affects them. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the optical spectral function and self-energy.

Xinxin Yang, Bohao Wu, Yu Chen +1 more

The f-sum rules set general constraints on the response of a quantum many-body system to an external probe and hold significant relevance in the realm of various spectroscopy measurements. In practical conditions, a system unavoidably couples with the environment and acquires effective dissipation. In this Letter, we derive and prove a set of f-sum rules for dissipative systems. Within the framework of linear response theory, we obtain the system response in both linear order of probe field and dissipation parameter. We formulate and prove one first-order and two second-order dissipative f-sum rules. These rules are validated numerically for some example models, and the realization schemes are proposed. In addition, the potential applications are discussed for two interacting many-body systems.