Relationship between negative differential thermal resistance and ballistic transport

In previous paper (Zhong W.-R. et al., Phys. Rev. E, 79 (2009) 050103(R)), it had been found that in the two-segment Frenkel-Kontorova (FK) model, transition from the exhibition to the nonexhibition of negative differential thermal resistance (NDTR) is consistent with the crossover from the ballistic to diffusive transport. It seems that the NDTR is induced by ballistic transport. When we further study ballistic transport in the two-segment Morse on-site potential model, it is found that no crossover from the ballistic to diffusive transport occurs accompanying transition from the exhibition to the nonexhibition of NDTR. There is always ballistic transport. Therefore, ballistic transport is not the sufficient condition of NDTR