RWTH- Aachen
Understanding the transport properties of correlated electron systems coupled to leads beyond the linear response regime (small bias voltage) is one of the main challanges in nonrelativistic quantum many-body theory. A rather limited number of nonperturbative methods is available which allow to tackle this problem in a controlled way. I will discuss the finite bias, steady-state transport through two different types of nanoscopic to mesoscopic systems in which correlation effects play a prominent role: a simplified model for one-dimensional quantum wires and an even more simplistic model for quantum dots (the interacting resonant level model). In the former the finite bias voltage leads to a real nonequilibrium effect in the steady state transport, while in the later the main features of the current versus voltage characteristics can be understood from the behavior in the linear response regime, at least if the correlations do not become too strong. The outcome of our approximate calculations is compared to the results obtained within alternative approaches.