Influence of the long-range interaction on the energy localization in 1D chain with an impurity

We investigate the influence of long-range interactions on the energy localization in a one-dimensional Morse chain with an impurity by molecular dynamics simulations. The energy distribution around the impurity is studied. It shows that in the high temperature limit there is no difference upon the potential energy localization whether the interaction includes a long-range one or not; but at low and intermediate temperatures, the difference is obvious. When the long-range interaction is taken into account, in the low temperature limit the potential energy localization is limited to the impurity and its next-nearest-neighbor particles, and the localization does not occur at its nearest-neighbor sites; in the intermediate temperature range, the potential energy localization takes place at the impurity and its nearest-neighbor sites, as well as the next-nearest-neighbor sites. The average potential energies 〈ui〉 and 〈u〉 of the impurity and host particles, respectively, are also investigated. The results show that corresponding to the soft (hard) impurity, at low temperatures, 〈ui〉 is lower (higher) than 〈u〉 and the softer (harder) impurity leads to lower (higher) 〈ui〉; however, at high temperatures, 〈ui〉 is higher (lower) than 〈u〉 and increases (decreases) with decreasing (increasing) stiffness of the impurity. The results are explained by the soliton fusion theory of Toda lattice.