Non-equilibrium current and electron pumping in nanostructures

We discuss a numerical method to study electron transport in mesoscopic devices out of equilibrium. The method is based on the solution of operator equations of motion, using efficient Chebyshev time propagation techniques. Its peculiar feature is the propagation of operators backwards in time. In this way the resource consumption scales linearly with the number of states used to represent the system. This allows us to calculate the current for non-interacting electrons in large one-, two- and three-dimensional lead-device configurations with time-dependent voltages or potentials. We discuss the technical aspects of the method and present results for an electron pump device and a disordered system, where we find transient behaviour that exists for a very long time and may be accessible to experiments.