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Nonequilibrium current driven by a step voltage pulse: an exact solution

One of the most important problems in nanoelectronic device theory is to estimate how fast or how slow a quantum device can turn on/off a current. For an arbitrary noninteracting phase-coherent device scattering region connected to the outside world by leads, we have derived an exact solution for the nonequilibrium, nonlinear, and time-dependent current driven by both up- and down-step pulsed voltages. Our analysis is based on the Keldysh nonequilibrium Green's functions formalism where the electronic structure of the leads as well as the scattering region are treated on an equal footing. A model calculation for a quantum dot with a Lorentzian linewidth function shows that the time-dependent current dynamics display interesting finite-bandwidth effects not captured by the commonly used wideband approximation.