Energy Transport in the Quantum Harmonic Chain in Contact with Phonon Reservoirs

We study energy transport in the quantum harmonic chain whose ends are in contact with two heat reservoirs at different temperatures. On the assumption that the reservoirs are composed of an infinite number of independent harmonic oscillators we derive the master equation that governs the time evolution of the reduced density matrix for the system. Mean kinetic energy of each particle and energy flux are calculated by perturbation with respect to the coupling constant. In the leading order obtained is the same bulk behavior as in the quantum Langevin approach. However, temperature profile near the ends is different due to contributions from higher-order terms when temperature is high and the reservoirs are non-Ohmic. The classical