Abstract: 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.

Key words: low-dimensional lattice, heat conduction, diffusion