Dynamic correlation functions for integrable mobile impurities

Abstract

We consider dynamical correlation functions near a spectral threshold in one dimensional quantum liquids. By using the phenomenological depleton model of mobile impurities we recover semiclassically the known leading power law behaviour of the correlation functions and express the corresponding edge exponents in terms of two phenomenological parameters: the number of depleted particles, \(N\) and the superfluid phase drop \(\pi J\). For integrable Lieb-Liniger and Yang-Gaudin models we establish a rigorous relation between these parameters and the Bethe Ansatz shift functions of elementary excitations. This relation implies the absence of phonon back scattering from integrable impurities.