Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid

We consider the motion of an impurity particle in a general one-dimensional quantum fluid at zero temperature. The dispersion relation Omega(P) of the impurity is strongly affected by interactions with the fluid as the momentum approaches +/-pi hn,+/- 3 pi hn,..., where n is the density. This behavior is caused by singular +/- 2 pi hn scattering processes and can be understood by analogy to the Kondo effect, both at strong and weak couplings, with the possibility of a quantum phase transition where Omega(')(+/-pi n) jumps to zero with increasing coupling. The low energy singularities in the impurity spectral function can be understood on the same footing.