  We calculate the conductance of a system of two spinless Luttinger liquid
wires with different interaction strengths g_1, g_2, connected through a short
junction, within the scattering state formalism. Following earlier work we
formulate the problem in current algebra language, and calculate the scale
dependent contribution to the conductance in perturbation theory keeping the
leading universal contributions to all orders in the interaction strength. From
that we derive a renormalization group (RG) equation for the conductance. The
analytical solution of the RG-equation is discussed in dependence on g_1, g_2.
The regions of stability of the two fixed points corresponding to conductance
G=0 and G=1, respectively, are determined.
