Time-dependent quantum current for independent electrons driven under nonperiodic conditions

An expression for the computation of the current in phase-coherent devices driven under arbitrarily time-dependent conditions is presented. The approach is developed for independent electrons in the time domain within a first-quantization formalism. The time-dependent current is computed by generalizing the Ramo-Shockley theorem to quantum systems. It is shown that the time-dependent conductance is not proportional to the quantum transmission coefficient, but to a parameter named the quantum current coefficient. As a test, it is proved that the present approach leads to the well-known Landauer model when static potentials are considered. As a simple numerical example, coherent quantum pumping is studied and applications for nanoscale solid-state field-effect transistors are predicted. © 2005 The American Physical Society.