Heat flow calculation for a harmonic model of a one-dimensional crystal

A one-dimensional non-dissipative harmonic chain of particles is considered, located between two thermal reservoirs. Using the fundamental solution of the one-dimensional harmonic model, an analytical representation is obtained for the discrete expression of the heat flux. Time averaging was performed, which allows taking into account the stationary characteristics of the heat transfer process. It is shown that the averaged heat flux includes two physically different components. The first one is proportional to the temperature difference between the reservoirs and characterizes the heat transfer along the chain. The second one determines the initial value of the flow when the temperatures of the tanks are equal.