一类一维非线性晶格热扩散与热传导行为研究

Heat Diffusion and Conduction in a One-dimensional Nonlinear Lattice Model

研究了一维类Toda晶格模型中有限温度下的能量、热量、动量、质量密度涨落弛豫和扩散的性质,并讨论了其与系统热传导行为的联系.发现低温下此模型的势函数退化为Toda势,其扩散和输运行为类似于可积的Toda晶格模型,扩散过程趋于弹道扩散,热传导行为不遵从傅里叶热传导定律;高温下则由于势函数的非对称性以及不可积性迅速增强,使得在一个很大的温度范围内热密度和能量密度扩散都表现出正常扩散特征.这一发现首次表明了非对称相互作用能导致动量守恒的系统表现出正常扩散行为,从而对这类系统能表现出正常热传导提供了微观机制的支持.

This paper studies the properties of relaxation and diffusion of energy, heat, momentum, and mass density fluctuations in a one-dimensional Toda-like lattice model at finite temperature, and discusses their relationship to the thermal conductance of the system. It is found that the interatomic potential function of this kind of lattice shows the Toda potential at low temperature, and that consequently the class of lattice appears the behavior of the integrable Toda lattice, such as diffusion tending to ballistic and heat conduction not satisfying the Fourier law, which lead to abnormal diffusion and heat conduction. The asymmetry of the potential function and the nonintegrability are rapidly enhanced with the temperature increased, thus the fluctuation of heat and energy density exhibit normal diffusion characteristics in a large temperature range. This result shows that the asymmetric interaction can lead to normal diffusion behavior in a one-dimensional momentum-conserving lattice, and the finding provides a micro-mechanism support to the phenomena that this class of system presents normal heat conduction.