Quantum thermal transport through anharmonic systems: A self-consistent   approach
  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. 
Dahai He and Juzar Thingna and Jian-Sheng Wang and Baowen Li
cond-mat.stat-mech quant-ph