Scaling behavior in a quantum wire with scatterers

We study the conductance properties of a straight two-dimensional quantum wire with impurities modeled by $s$-like scatterers. Their presence can lead to strong inter-channel coupling. It was shown that such systems depend sensitively on the number of transverse modes included. Based on a poor man's scaling technique we include the effect of higher modes in a renormalized coupling constant. We therefore show that the low-energy behavior of the wire is dominated by only a few modes, which hence is a way to reduce the necessary computing power. The technique is successfully applied to the case of one and two $s$-like scatterers.