Energy Diffusion And Finite Time Thermal Conductivity In A One-dimensional Diatomic Ideal Gas

Diffusion is one basic motion.The study of diffusion can be traced back to the description of Brownian motion.Initially,Einstein proposed the famous Einstein relation on the basis of the random walk hypothesis.For the first time,the microcosmic motion of the particles was linked to the macroscopic transport process of the system,the relationship between particle diffusion and viscosity was established.Subsequently,Ryogo Kubo proposed that the Brownian motion can be seen as the response of the system which is subjected to the external disturbance,and then proposed the theorem of fluctuation-dissipation.The theorem promoted the Einstein relation,laid the foundation of modern transport theory.The reliability of these theories has been extensively tested in the macroscopic system.In recent decades,low dimensional materials have got widespread research due to the novel properties and the potential application.However,a fully understand to the basic physical laws of such system is still lacks,such as the phenomenon of anomalous heat conduction.Although a great deal of research has been done,people still cannot completely understand the heat conduction law which the low-dimensional system followed,let alone understand the microcosmic mechanism of these anomalies.The generally accepted view is that,the heat transport of the low-dimensional system does not satisfy the Fourier law,and the traditional transport theory which is based on the particle diffusion also cannot give a satisfactory explanation of these anomalous heat conduction phenomena.Based on this,people began to study the energy diffusion in low-dimensional systems,in order to understand the microcosmic mechanism of the above-mentioned anomalous heat conduction,thus improve the traditional transport theory,to make it suitable for describing the low-dimensional system.Differs from the particle diffusion,the energy diffusion in equilibrium state cannot be directly observed by experiment.People mainly use the method of numerical simulation to study the energy diffusion.There are two methods.One is to observe the relaxation process of non-equilibrium perturbation.Another method is to calculate the spatiotemporal correlation function in the equilibrium state.In this paper,we use an effective method to study energy diffusion in 1D diatomic ideal gas at equilibrium state,in order to track the evolution of energy diffusion in real space.By using the linear feature of the evolution equation of this system,a companion system is constructed for the numerical simulation,in order to track the direct evolution of the energy in the real space.The energy probability density function and the energy diffusion index of the one-dimensional diatomic ideal gas with different mass ratio are calculated by this method.It is found that in such a system the energy diffusion depends on the mass ratio of the two atoms:1)For larger mass ratio,the probability density function of energy diffusion is consistent with L6vy distribution.The energy diffusion index ? satisfies with1<?<2,belonging to super diffusion.2)For smaller mass ratio,however,probability density function tends to Gaussian distribution.We obtained that??1 at long time scale,belonging to normal diffusion;??2 at short time scale,belonging to ballistic diffusion.In addition,the energy diffusion index ? is calculated when the pressure of the 1D diatomic chain is zero.It is found that the energy diffusion index of the system under different mass ratio is always ??1,belonging to normal diffusion.Furthermore,in order to verify the quantitative relationship between the divergence index of the thermal conductivity and the energy diffusion index found by the predecessors,the finite thermal conductivity of 1D diatomic ideal gas is calculated.