Quasi-thermalization And Heat Diffusion In One-dimensional Lattices With Long-range Interactions

Long-range interactions are present at various scales in nature.As a result of the lack of additivity in systems with long-range interactions,both thermodynamic and dynamic properties of these systems are very different from the traditional Gibbs statistical physics with short-range interactions.Energy equipartition can be established in short-range systems after dynamic process of thermalization.However,energy redistribution among different degrees of freedom in systems with long-range interactions is unclear.We study the quasi-thermalization and the heat diffusion law of the one-dimensional long-range FPUT-?model by molecular dynamics method.The strength of interactions between particles in the system with long-range interactions decreases with the increase of the distance between particles in the way of distance-?(??0).As the increase of the attenuation exponent ?,we find that the transition process of mode-energy distribution from localized to equipartitioned.In particular,a obviously transitions of mode-energy distribution from strong long-range coupling to weak long-range coupling is observed around the value ?=1.By taking the temporal fourier transform of the different normal-mode energies,we find that the varying power spectrum overlapping among vibration modes is responsible for this phenomenon.Through further calculation of spectral entropy,the minimum duration of quasi-stationary states(QSS)?QSS is found at the value ?=2,which may provide explanations for peculiar behavior of heat transport in long-range lattice chains.In further understand the special thermal transport phenomena exhibited in the one-dimensional long-range FPUT-? model,we also analyze the spatiotemporal correlation function of energy density fluctuations of long-range systems and the rescaling exponent y with different values of ? from the perspective of diffusion.We observe a dynamic change of the shape of the heat and sound mode peaks in the spatial distribution of the energy density fluctuation correlation function of the system with the increase of the attenuation exponent ?,indicating that the roles of thermal and acoustic modes in the energy diffusion process have changed.There is a non-monotonic dependence between the rescaling exponent y and the exponent ?.The range of the exponent y is between the normal diffusion exponent and the ballistic diffusion exponent,and reaches the ballistic diffusion exponent 1 when ?=2,indicating that the energy diffusion behavior of the system changes significantly with the increase of the exponent ?.Our results not only contribute to understanding the dynamics of energy relaxation and the anomalous heat transport phenomena in long-range systems but also shed light on the long-standing problem of thermalization and low-dimensional thermal transport in short-range systems.We expect that our conclusions can provide some theoretical help for the thermal management in low-dimensional materials.