System-Environment Entangled Optical Absorption Spectrum And Heat Fluctuation Spectrum

For the actual systems that are of interest in physics,chemistry,and biology,it often contains a lot of degrees of freedom.In principle,its dynamic behavior can always be obtained by solving the Schrodinger equation containing all degrees of freedom.How-ever,due to computational impracticality,in practice we always select a small number of interested degrees of freedom as the system,and the rest as the environment of the system.As a result,we can always turn the problems of complex systems into prob-lems of system-bath interaction.Therefore,the entangled nature of system-bath plays a very important role in studying the behavior of complex systems,especially its quantum behavior.In this article,based on the quantum Langevin equation,we focus on two recent studies related to system-bath entanglement.First,for any system coupled with the Gaussian environment,we established the "system-bath entanglement theorem".The theorem shows that as long as the environmental spectral density function of the inter-action is given,the system-bath entanglement response function can be connected with the system-system local response function.This theorem enables dynamic methods that focus only on the system itself,such as quantum master equation theory,etc.,can also be used to calculate and study the entanglement characteristics of the system-bath.As an example,we use this theorem to numerically simulate the Fano interference effect in the light absorption spectrum.The simulation results are completely consistent with the results of the dissipaton equation of motion;the dissipaton equation of motion is a rigorous method for studying the dynamics of system-bath entanglement.The system-bath entanglement theorem is established between the response func-tions,and it is applicable to both the equilibrium state and the nonequilibrium steady state.For a system in an equilibrium state,the entanglement relationship between corre-lation functions can be directly obtained by the fluctuation-dissipation theorem.How-ever,for the non-equilibrium steady state,the failure of the fluctuation-dissipation the-orem makes this type of relationship impossible.Therefore,we return to the quantum Langevin equation and obtain a strict expression of the nonequilibrium steady-state correlation function at time zero.The results we have obtained not only provide a new perspective for the nonequilibrium Green's function theory,but also lay a solid founda-tion for the further study of quantum nonequilibrium thermodynamics.As an example,combined with the dissipative equation of motion method,we study the problem of nonequilibrium heat transport.Through these theoretical tools,we have calculated and studied the most critical physical quantities in quantum heat transport——heat flow and thermal fluctuation spectrum,which collectively reflect the entanglement characteris-tics of the system and the environment.