  We present a formulation of a nonequilibrium Green's function method for
thermal current in nanojunction atomic systems with nonlinear interactions.
This first-principle approach is applied to the calculation of the thermal
conductance in carbon nanotube junctions. It is shown that nonlinearity already
becomes important at low temperatures. Nonlinear interactions greatly suppress
phonon transmission at room temperature. The peak of thermal conductance is
found to be around 400K, in good agreement with experiments. High-order phonon
scattering processes are important for diffusive heat transport.
