Impurities in a one-dimensional Bose gas: the flow equation approach

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend approach to compute observables other than energy. As an example, calculate densities, phase fluctuations one-dimensional one two For single mobile impurity, use validate mean-field results obtained upon Lee-Low-Pines transformation. We show that approximation is accurate all values boson-impurity interaction strength long coherence length much larger healing condensate. static impurities, impurity-impurity interactions induced by gas. find leading order perturbation theory fails when are stronger boson-boson interactions. The reproduces equation weak.