Non-equilibrium ensemble theory for thermal transport in anharmonic crystals

We propose an ensemble theory for the non-equilibrium statistics to study the thermal transport in anharmonic crystals. In the theory, lattice vibrations of the crystals are quantized by local Bosons(LBs), instead of Phonons as usually used for the thermal transport. LBs are driven by the temperature gradient and move from atom to atom in the crystals. Based on the LBs, anharmonic interactions between atoms in the crystals can be fully considered. To demonstrate our theory, we study the thermal transport in an atomic chain with a temperature drop applied on the two ends of the chain. We observe a Rabi-like oscillation in the transport of the LBs, from which we define the thermal current to get the thermal conductivity of the chain. Results show that the thermal conductivity is enhanced slowly with the increasing of the anharmonic interaction and decreases rapidly if the anharmonic interaction is increased further. In the present study, we only focus on the steady state, and the fluctuations of the thermal currents are not considered.