Heat conductivity in the presence of a quantized degree of freedom

We propose a model with a quantized degree of freedom to study the heat transport in quasi-one dimensional system. Our simulations reveal three distinct temperature regimes. In particular, the intermediate regime is characterized by heat conductivity with a temperature exponent $\gamma$ much greater than 1/2 that was generally found in systems with point-like particles. A dynamical investigation indicates the occurrence of non-equipartition behavior in this regime. Moreover, the corresponding Poincar\'e section also shows remarkably characteristic patterns, completely different from the cases of point-like particles.