The momentum- and frequency-dependent correlation functions (one-body and density-density) of the one-dimensional interacting Bose gas (Lieb-Liniger) are obtained for any value of the interaction parameter. In the repulsive regime, we use a method that mixes algebraic Bethe ansatz and numerics to reconstruct the correlators to high accuracy for systems with finite but large numbers of particles. For attractive interactions, the correlations are computed analytically. Our results are discussed, with particular emphasis on their applications to quasi-one-dimensional atomic gases.

Universita di Pisa