Diffusion Property In One-dimensional Nonlinear Lattice

Low-dimensional materials have become the forefront of many natural sciences.It has been accepted that the study of the diffusion properties at finite temperature is of great theoretical significance for revealing the physical behavior of non-equilibrium statistics of low-dimensional systems and understanding the micro-mechanism of heat conduction.In this paper,we investigate the diffusion properties of fluctuation of energy,heat,momentum,and mass density,as well as their relations to macroscopic heat conduction behavior in a special class of one-dimensional nonlinear lattice.In this paper,we first introduce the background and the main achievements of heat conduction of low-dimensional lattices both in theory and experiment,and then report some main results achieved in the numerical simulation of a class of asymmetric one-dimensional lattice,namely Toda-like lattice models.These results include:(1)Due to the particularity of the potential function,the class of lattice appears the behavior of the integrable Toda lattice model,such as diffusion tending to ballistic and heat conduction not satisfying the Fourier law,which lead to abnormal difusion and heat conduction.(2)The asymmetric interaction potential at high temperature increases rapidly,which makes the diffusion of local fluctuation of heat and energy density show characteristics of normal diffusion in a large temperature range.It is first verified that the asymmetry of the interatomic potential function can render momentum-conserving systems involved with normal thermal diffusion,which thus provides a micro-mechanism support for such a system that can actually exhibit normal heat conductiom.This finding is of great significance to understand the law of fluctuation and relaxation,as well as the microscopic mechanism of transport behavior in low-dimensional systems.At the end of this paper,we summarize the research results.