Unusual Anomalous Heat Spread Contributed by Optical Phonon-Phonon Interactions

We employ the equilibrium correlation functions to study heat spread in an anharmonic chain subject to a \emph{harmonic} pinned potential. Such a system is nonacoustic with purely deterministic dynamics, while previously, due to the momentum-nonconserving feature, it was naturally thought to follow the normal diffusive transport. Here, instead, we find that, the heat spread is superdiffusive, yet implying the anomalous transport. In particular, a non-Gaussian truncated L\'{e}vy walk heat spreading function with anomalous scaling is, for the first time, observed, and the underlying mechanism is related to a novel effect of optical phonon-phonon interactions. As most of the current theories for deterministic dynamics are mainly based on the long-wavelength acoustic phonons, and for the pinned systems normal transport was always predicted, our results may open new avenues for further exploring thermal transport.