Analysis Of Heat Transport In A Nonequilibrium Spin-boson Model

In recent years,the heat transport of non-equilibrium spin-boson systems has aroused great interest in the fields of condensed matter physics,chemical physics and biophysic-s.Non-equilibrium spin-boson system consists of a spin system immersed in two(or more)dissipative environments with different chemical potentials or temperatures.By studying the properties of heat transport in the non-equilibrium spin-boson model can provide a theoretical support for many related experiments.Many analytical and numerical methods have been developed to study this prob-lem.Although each method has its own advantages and disadvantages,an analytical method can provide a more clear physical picture than a purely numerical method,and it can help us deeply understand the nature of heat transport.In this paper,we study the effect of the environmental temperature as well as the system-environment cou-pling strength on the heat transfer in the nonequilibrium spin-boson model.First,we can use the Keldysh Green's function to obtain the general expressions of the ther-mal current and the thermal conductance,however,the expressions still contain the dy-namical susceptibility which is difficult to handle.We present a perturbative approach which combines a generalized polaron transformation and a resolvent operator expan-sion technique to solve this difficulty.Using this method,we analytically obtained the specific expressions of the thermal current and the conductance of the non-equilibrium spin-boson model.We find the thermal current J and the conductance?show a lin-ear growth trend with increasing of the coupling strength in the weak coupling regime.When the coupling becomes stronger,they exhibit certain nonlinear characteristics.In the low temperature range,the conductance is proportional to T~3.As the temperature increases,this T~3-law collapses.