Linear Response Theory Of Composite System And Its Application

In recent years,response theory has aroused great interest due to its extensive applications in many fields,such as biophysics,nanophysics,and condensed matter physics.In 1957,Japanese physicist Ryogo Kubo studied the response theory and deduced the change of the mechanical quantity of the system with the weak external field.The external field is weak,the basic properties of the system will hardly change,but the mechanical quantity will change with the external field.This change can be expanded into the form of the series of the external field.The coefficient of the first-order term of the series is called the response coefficient.This theory is called the linear response theory.The response coefficient is usually time-dependent,which can give the susceptibility through a Fourier transform.The frequency dependence of the imaginary part of the susceptibility has a fixed line width.The energy spectrum structure of the system can be solved by this line width.Therefore,the information of the system can be obtained indirectly by measuring the susceptibility.The main part of this paper is to study the linear response theory of composite system.In fact,the research on response theory of composite systems start very early.Most scholars focus on the information of the whole system,but I focus on the subsystem of the composite system.The model is composed of two subsystems.Perturb subsystem 1,subsystem 2 will generate a response.I will use the susceptibility as an example.Based on the Kubo formula,I first derive the expression of the susceptibility of subsystem 2.The imaginary part of the susceptibility depends on frequency,so it is more meaningful for study.Therefore,the real and imaginary parts of the susceptibility are separated.I find that the imaginary part of the susceptibility of subsystem 2 depend on energy and it can be expressed as a ? function.In order to explain my conclusions more intuitively,I apply this theory to two coupled two-level systems,and give the frequency dependence of the imaginary part of the susceptibility of the subsystem 2.Under different temperature parameters and coupling strength parameters,its energy spectral lines are analyzed.It is found that the position of the peak of the imaginary part of the susceptibility is just the energy level difference,and the difference is only related to the coupling strength.Our results provide theoretical support for coherent manipulation of composite system and have potential applications in quantum information processing and statistical physics.The system studied in this paper is time-independent,and our next work is to continue to study the response of the time-dependent composite system.