Center deviation of localized modes in a one-dimension anharmonic single impurity chain

A 1D anharmonic chain with a single impurity particle is used to study the center deviation and stability of the localized modes. The displacement patterns of the localized modes for a variable impurity mass and anharmonic parameter are studied. The pattern center is shifted away from the impurity with decreasing anharmonic parameter for both symmetric and asymmetric anharmonic impurity modes. In the limit of a heavy-mass impurity, the energy localization is constrained to the three particles nearest to the impurity.