Equilibrium Dissipation Of Nonlinear Wave Packets In A One-dimensional FPU Lattice System

In recent years,it is possible to make the scientists measure the energy transport of low-dimensional materials with the development and perfection of experimental technology.So many anomalous heat conduction phenomenons have been found.For example,the thermal conductivity of the low-dimensional system increases with the size of the system;some asymmetric heat conduction phenomenons occur in some non-uniform systems.Although these anomalous phenomenons correspond with the prediction of traditional theory qualitatively,their micro dynamics mechanisms are still unclear.So it has become one of the research hot spots of non-equilibrium statistical physics.In the courses of the theoretical researches on the micro dynamical mechanism of anomalous heat conduction,the one-dimensional Feimi-Pasta-Ulam(FPU)lattice system was found to be an appropriate and useful theoretical model,and it was widely and deeply discussed.Existing research results show that not only linear waves(phonons)but also nonlinear waves(solitons and breathers)can be excited in FPU lattice systems.With the deepening of the study,some scholars believe that the nonlinear waves play a vital role in the anomalous heat conductions,but some scholars argue that research achievements about the dynamics of nonlinear wave are mainly under the absolute zero degree.They think there is no direct evidence that nonlinear wave still exists in finite temperature system.Therefore,it is doubtful whether the nonlinear wave participates the energy transport of the system or how much degree of participation dose the nonlinear wave have.In this paper,the damping law of nonlinear wave packets in one-dimensional FPU-??lattice at finite temperature is studied by numerical simulation.The results show that the energy of the nonlinear wave packets decays with the power law of the time when they transport in the thermal environment.It shows there may be long-life nonlinear wave packets which affect the energy transport of the system in the system at finite temperature.At the same time,the influence of excitation momentum,system temperature and the symmetry of the interaction between particles on the characteristic time of the damping of the nonlinear wave packet is also calculated in detail.The results show that:1)the characteristic time varies with excitation momentum according to the index law,and the higher the excitation momentum,the longer the life of the nonlinear wave packet;2)the characteristic time changes with the temperature according to the power law,and the lower the temperature,the longer the life of the nonlinear wave packet;3)the characteristic time increases exponentially with the increase of asymmetry parameters,and the higher the symmetry,the longer the life of the nonlinear wave packet.The results will be instructive to understand the micro dynamical mechanism of anomalous heat conduction in low-dimensional systems.