  We investigate quantum heat transfer and thermal management in the
nonequilibrium qubit-phonon hybrid system by applying the quantum master
equation embedded with phononic coherent state. We obtain the steady state heat
flow by tuning the arbitrary qubit-phonon coupling strength, which particularly
exhibits the power-law scaling behavior and the turnover behavior in the weak
and strong coupling regimes, respectively. Moreover, we analyze the negative
differential thermal conductance and thermal rectification, which becomes
profound with weak qubit-phonon interaction and large temperature bias. These
results would contribute to smart energy control and design of phononic hybrid
quantum devices.
