Friedel Oscillations in Luttinger Liquids Reinhold Egger and Hermann Grabert

We study the density disturbance of a correlated one–dimensional electron liquid in the presence of a scatterer or a barrier. The 2kF – periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron–electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi liquid theory. In the case of a spinless Luttinger liquid characterized by an interaction constant g ≤ 1, the asymptotic decay of the Friedel oscillation is x−g. For a weak scatterer, the decay is even slower at small–to–intermediate distances from the impurity, with a crossover to the asymptotic x−g law.