Crossover from Ballistic to Diffusive Thermal Transport in Carbon Nanotubes

We present a theoretical scheme that seamlessly handles the crossover from fully ballistic to diffusive thermal transport regimes and apply it to carbon nanotubes. At room temperature, the micrometer-length nanotubes belong to the intermediate regime in which ballistic and diffusive phonons coexist, and the thermal conductance exhibits anomalous nonlinear tube-length dependence due to this coexistence. This result is in excellent agreement with molecular-dynamics simulation results showing the nonlinear thermal conductance. Additionally, we clarify the mechanism of crossover in terms of characteristic frequency, which is a new concept derived from the scheme.