  We propose a feasible and effective approach to study quantum thermal
transport through anharmonic systems. The main idea is to obtain an {\it
effective} harmonic Hamiltonian for the anharmonic system by applying the
self-consistent phonon theory. Using the effective harmonic Hamiltonian we
study thermal transport within the framework of nonequilibrium Green's function
method using the celebrated Caroli formula. We corroborate our quantum
self-consistent approach using the quantum master equation that can deal with
anharmonicity exactly, but is limited to the weak system-bath coupling regime.
Finally, in order demonstrate its strength we apply the quantum self-consistent
approach to study thermal rectification in a weakly coupled two segment
anharmonic system.

Statistical Mechanics;Quantum Physics