Here I tried to analiticaly reproduce the phonon spectral function (Fig. 4d) of a 1D-chain model showing some elementary ferroelectric domain wall modes (the nondispersive sliding mode at the lowest energy, the breathing mode at a higher energy, and the dispersive bulk phonon branch) of [Sci. Adv. 3, e1602371 (2017)].
Here will come some introductions…