Path-integral approach to transient transport of a double-barrier resonant-tunneling system

Based on a many-body tunneling Hamiltonian for a double-barrier resonant-tunneling system, we demonstrate the evolution of the tunneling current in terms of the nonequilibrium distribution, spectrum, and dissipation of tunneling electrons. We find two time scales relevant to the transient process: the lifetime of resonance level (${\mathrm{\tau }}_{\mathit{R}}$) and the dissipation time (1/ν) of electrons in the two leads. ${\mathrm{\tau }}_{\mathit{R}}$ is determined as a function of the dissipation of lead electrons as well as the barrier profile, including the bias effect.