  Within the framework of boundary conformal field theory, we evaluate the
conductance of stable fixed points of junctions of two and three quantum wires
with different Luttinger parameters. For two wires, the physical properties are
governed by a single effective Luttinger parameters for each of the charge and
spin sectors. We present numerical density-matrix-renormalization-group
calculations of the conductance of a junction of two chains of interacting
spinless fermions with different interaction strengths, obtained using a
recently developed method [Phys. Rev. Lett. 105, 226803 (2010)]. The numerical
results show very good agreement with the analytical predictions. For three
spinless wires, i.e., a Y junction, we analytically determine the full phase
diagram, and compute all fixed-point conductances as a function of the three
Luttinger parameters.
