Elastic transient energy transport and energy balance in a single-level quantum dot system

We derive a nonequilibrium Green's function formalism to study the transient energy currents carried by electrons in a single-level quantum dot system sandwiched between two electrodes. The energy current shows the same relaxation time and oscillation behavior as the electrical current. In contrast to the steady state case, the energy currents in deep insides of the two electrodes do not balance each other in the time domain. The sum of energy currents in the two electrodes corresponds to the time-dependent energy change in the sandwiched region, and the fact that the energy change in this region is not necessarily zero reflects the real-time electron redistribution in energy domain. Moreover, the amplitude of the energy change does not vary monotonically with the coupling strength between the dot and electrode, in contrast to the relaxation time, which is inversely proportional to the coupling strength.