  We develop two novel numerical schemes to study the conductance of the
two-wire junction of inequivalent Tomonaga-Luttinger Liquids. In the first
scheme we use the static current-current correlation function across the
junction to extract the linear conductance through a relation that is derived
via the bosonization method. In the second scheme we apply a bias and evaluate
the time-dependent current across the junction to obtain the current-voltage
characteristic. The conductance is then extracted from the small bias result
within the linear response regime. Both schemes are based on the infinite size
matrix product state to minimize the finite-size effects. Due to the lack of
the translational invariance, we focus on a finite-size window containing the
junction. For time-independent calculations, we use infinite boundary
conditions to evaluate the correlations within the window. For time-dependent
calculations, we use the window technique to evaluate the local currents within
the window. The numerical results obtained by both schemes show excellent
agreement with the analytical predictions.
