  In this article, we address lattice heat transport in single-walled carbon
nanotubes (CNTs) by a quantum mechanical calculation of three-phonon scattering
rates in the framework of the Boltzmann transport equation (BTE) and classical
molecular dynamics (MD) simulation. Under a consistent choice of an empirical,
realistic atomic interaction potential, we compare the tube length dependence
of the lattice thermal conductivity (TC) at room temperature determined from an
iterative solution of the BTE and from a nonequilibrium MD (NEMD) approach.
Qualitatively similar trends are found in the limit of short tubes, where an
extensive regime of ballistic heat transport prevailing in CNTs of lengths
$L\lesssim 1\,\rm{\mu m}$ is independently confirmed. In the limit of long
tubes, the BTE approach suggests a saturation of TC with tube length, whereas
direct NEMD simulations of tubes extending up to $L=10\,\rm{\mu m}$ are
demonstrated to be insufficient to settle the question of whether a fully
diffusive heat transport regime and an intrinsic value of TC exist for CNTs.
Noting that acoustic phonon lifetimes lie at the heart of a saturation of TC
with tube length as per the BTE framework, we complement the quantum mechanical
prediction of acoustic phonon lifetimes with an analysis of phonon modes in the
framework of equilibrium MD (EMD). A normal mode analysis (NMA) with an
emphasis on long wavelength acoustic modes corroborates the BTE prediction that
heat transport in CNTs in the long tube limit is governed by the low
attenuation rates of longitudinal and twisting phonons.
