Energy Diffusion And Transport In One-dimensional Diatomic Ideal Gases

One of the basic question of non-equilibrium statistical physics is to calculate the macroscopic transport coefficient from the microstructure of the system and the motion of the microscopic particles.Einstein regarded Brown motion as a Markov process at first and obtain the transport coefficient of the system.Since then,researchers extended to other transport processes,developed methods and tools such as the fluctuation dissipation theorem and linear response theory,and established the basic framework of near-equilibrium statistical physics.The discovery of the"long-time tail" makes people aware of the limitations of the near-equilibrium statistical theory.In the past few decades,with the development of theory and the progress of experiments,researchers have discovered the so-called abnormal energy transport in low-dimensional materials,the phenomenon of exponential diverge of thermal conductivity as the system size increases,which violates Fourier law.This abnormal behavior cannot be explained by the existing non-equilibrium theory.Therefore,recently,many researchers have tried to imitate the ideas of particle transport to establish a connection between energy diffusion and heat conduction in low-dimensional systems,in order to reveal the microscopic dynamic mechanism of abnormal heat conduction phenomena.Based on the above facts,this article mainly uses molecular dynamics simulation method to study the energy diffusion behavior of the one-dimensional diatomic ideal gas mode with different mass ratios in equilibrium state,and the thermal conductivity of the system in the equilibrium and non-equilibrium states with the dependence of the system size.Especially the relationship between the energy diffusion exponent and the thermal conductivity divergence exponent.We found that as the mass ratio of the two particles changes,the system exhibits the following characteristics:（1）In the equilibrium state,the energy diffusion behavior of the system is related to the diffusion time,and as the mass ratio tends to be same,the system exhibits the following characteristics:The diffusion behavior under time changes from "super diffusion"（diffusion exponent β greater than 1 and less than 2）to "normal diffusion"（diffussion exponent β=1）;（2）As the mass ratio tends to be same,the flow correlation function under equilibrium gradually transform from "power law decay" to"exponential decay" over time,that means the heat conduction of the system has a transition from abnormal to normal according to the Green-Kubo formula in the linear response theory;（3）Under non-equilibrium state the calculation shows that the heat conduction behavior of the system changes with the system size,showing an abnormal heat conduction behavior.The thermal conductivity diverges with the system size exponent under a large mass ratio,but tends to a certain constant value under a small mass ratio,which is in line with the equilibrium state.The following calculation results are qualitatively consistent;（4）The thermal conductivity divergence exponent and the energy diffusion exponent of the system show a non-monotonic dependence.This result does not agree with the theoretical predictions of several monotonic changes given by previous authors.We study the energy diffusion and heat transport of the one-dimensional diatomic ideal gas mode in molecular dynamics simulation methods.The research results are useful and have reference value for exploring the dynamic mechanism of abnormal heat conduction behavior in low-dimensional systems,and improving and developing non-equilibrium statistical theories.