Effect of dynamical localization on negative differential thermal resistance

We numerically study heat conduction in a homogeneous lattice of interacting oscillators via analyzing the power spectrum of system's vibrations. The mechanism for the presence and the size effect of negative difference thermal resistance (NDTR) is understood based on dynamical localization of phonon modes. Localized modes are clearly shown in the spectra when large temperature difference is applied to the system. And then we propose a quantitative analysis for the relation between NDTR and the localization in a phenomenological way, which indicates that NDTR can be obtained in a small system with system size less than the localization length and explain the saturation of heat flux. The theoretical calculations are consistent with numerical simulations.