The Heat Conduction Of One-Dimensional Lennard-Jones Gas

In recent decades, low-dimensional nano-materials and systems have been research frontiers in many fields of science, in which study of heat conduction in low-dimensional systems is of fundamental significance. Heat conduction in three-dimensional macroscopic materials can be described by the famous Fourier’s law, i.e., the heat flow is proportional to the temperature gradient▽T, where k, heatconductivity, is intrinsic property of materials, irrespective of the size of material. Although the Fourier’s law has been widely verified for three-dimensional cases, it is not experimentally conclusive for low-dimensional systems basically due to the precision of measurement in lab nowadays. On the other hand, results of theoretical analysis and molecular dynamical simulations of previous studies show that heatconductivity of momentum-conserving low-dimensional systems increases as the system size increases and diverges in the thermodynamic limit. However, the complex-system group of Xiamen University recently suggests that the asymmetry of the interaction potential plays a key role for the behavior of heat conduction. They show that normal conduction can be obtained for a system of asymmetric interaction potential based on extensive studies in several exemplified low-dimensional models, one of which is the one-dimensional lattice system with Lennard-Jones potential.The main purpose of the presented thesis is to study the behavior of the heatconductivity of one-dimensional momentum-conserving gas model with Lennard-Jones potential. We compute the relaxation behavior of the heat flow’s correlation function in the equilibrium state and then apply the Green-Kubo formula to calculate the heatconductivity. In order to verify the conclusion, we also use non-equilibrium molecular dynamical simulation to calculate the size dependence of thermal conductivity in a direct way. The main conclusion of the thesis is that the decay behavior of the flux correlation of the one-dimensional gas system with Lennard-Jones potential contains two time scales. The flux correlation exhibits a very rapid exponential-decay process in the first time scale and then be subjected to a slower exponential decay in the second time scale which is much longer. The results not only show that the one-dimensional gas model with Lennard-Jones potential has normal heat conduction but also reveal the exact relaxation process of the system. If the rapid-decay process was neglected, the calculation of thermal conductivity by the Green-Kubo formula would be incorrect. In order to understand the underlying microscopic mechanism, we also study the dynamics of the collision of particles and find chaotic scattering, non-completely elastic scattering, elastic scattering and the transition process of energy with the collision in the system.