Local time-dependent perturbation in Luttinger liquid

The response of the Luttinger liquid to a local potential is studied at zero temperature. It exhibits a crossover behavior. On the largest time scale and in the case of repulsive electron-electron interaction, the backscattering from the potential contributes to the core-hole Green’s function G(t) the factor (${\mathit{t}}_0$/t${)}^{1/8}$—a universal (potential independent) decay law. The orthogonality catastrophe remains of the same analytical type as for the simple metals.