  We present a detailed treatment of the nonequilibrium Green's function method
for thermal transport due to atomic vibrations in nanostructures. Some of the
key equations, such as self-energy and conductance with nonlinear effect, are
derived. A self-consistent mean-field theory is proposed. Computational
procedures are discussed. The method is applied to a number of systems
including one-dimensional chains, a benzene ring junction, and carbon
nanotubes. Mean-field calculations of the Fermi-Pasta-Ulam model are compared
with classical molecular dynamics simulations. We find that nonlinearity
suppresses thermal transport even at moderately high temperatures.
