ABSTRACT

Quantum thermal transport in harmonic chains has been extensively studied as well as its classic counterpart [1]. One can use generalized Langevin approach [2], nonequilibrium Green’s function method (NEGF) [3] and density matrix approach [4] to study the harmonic model exactly. As far as anharmonicity is concened, the situation becomes complicated. In this case, the transport of phonon is no longer ballistic. Most of previous studies [3] are mainly in a perturbative manner, which cannot handle strong anharmonicity. A developed master equation approach has been proposed recently, which can deal with anharmonicity exactly in the weak coupling limit [5]. However, since ME is handled in the Hilbert space, which increases rapidly with temperature as well as the number of particles. Hence it is computationally expensive to deal with nano systems of 10-100 atoms. In this talk I will propose a feasible and effective approach for quantum thermal transport through anharmocic systems. The key idea here is to apply the self-consistent phonon theory (SCPT) to renormalize the anharmonic Hamiltonian to an effective harmonic Hamiltonian [6, 7, 8]. We then apply NEGF to study the effective harmonic model using the standard ballistic framework. The results show a good agreement with that by the master equation approach in the weak coupling limit [9].