  Numerical analysis of the spectrum of large finite size Luttinger liquids
(g<1) in the presence of a single source of 2k_f scattering has been made
possible thanks to an effective integration of high degrees of freedom.
Presence of irrelevant operators and their manifestation in transport are
issues treated independently. We confirm the existence of two irrelevant
operators: particle hopping and charge oscillations, with regions of dominance
separated by g=1/2. Temperature dependence of conductance is shown to be
dominated by hopping alone. Frequency dependence is affected by both irrelevant
operators.
