We show, using a tight-binding model and time-dependent density-functional theory, that a quasi-steady-state current can be established dynamically in a finite nanoscale junction without any inelastic effects. This is simply due to the geometrical constriction experienced by the electron wave packets as they propagate through the junction. We also show that in this closed nonequilibrium system two local electron occupation functions can be defined on each side of the nanojunction which approach Fermi distributions with increasing number of atoms in the electrodes. The resultant conductance and current-voltage characteristics at quasi-steady state are in agreement with those calculated within the static scattering approach.

So far transport properties of nanoscale contacts have been mostly studied within the static scattering approach. The electron dynamics and the transient behavior of current flow, however, remain poorly understood. We present a numerical study of microscopic current flow dynamics in nanoscale quantum point contacts. We employ an approach that combines a microcanonical picture of transport with time-dependent density-functional theory. We carry out atomic and jellium model calculations to show that the time evolution of the current flow exhibits several noteworthy features, such as nonlaminarity and edge flow. We attribute these features to the interaction of the electron fluid with the ionic lattice, to the existence of pressure gradients in the fluid, and to the transient dynamical formation of surface charges at the nanocontact-electrode interfaces. Our results suggest that quantum transport systems exhibit hydrodynamical characteristics which resemble those of a classical liquid.

Electron transport through a nanostructure can be characterized in part using concepts from classical fluid dynamics. It is thus natural to ask how far the analogy can be taken and whether the electron liquid can exhibit nonlinear dynamical effects such as turbulence. Here we present an ab initio study of the electron dynamics in nanojunctions which reveals that the latter indeed exhibits behavior quite similar to that of a classical fluid. In particular, we find that a transition from laminar to turbulent flow occurs with increasing current, corresponding to increasing Reynolds numbers. These results reveal unexpected features of electron dynamics and shed new light on our understanding of transport properties of nanoscale systems.

It was recently predicted [J. Phys. Condens. Matter 18, 11059 (2006)] that turbulence of electron flow may develop at nonadiabatic nanoscale junctions under appropriate conditions. Here we show that such an effect leads to an asymmetric current-induced magnetic field on the two sides of an otherwise symmetric junction. We propose that measuring the fluxes ensuing from these fields across two surfaces placed at the two sides of the junction would provide direct and noninvasive evidence of the transition from laminar to turbulent electron flow. The flux asymmetry is predicted to first increase, reach a maximum, and then decrease with increasing current, i.e., with increasing amount of turbulence.