FRIEDEL OSCILLATIONS FOR INTERACTING FERMIONS IN ONE-DIMENSION

We study Friedel oscillations in one-dimensional electron liquids for arbitrary electron-electron interaction and arbitrary impurity strength. Explicit results for spinless as well as spin-1/2 electrons are given. In the case of Luttinger-liquid leads, the Friedel oscillations decay as x(-g) far away from the impurity where g is the interaction constant. For a weak scatterer, a slower decay is found at small-to-intermediate distances from the impurity, with a crossover to the asymptotic x(-g) decay.