Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

In this paper we study the non-equilibrium dynamics of one-dimensional Bose gas from the general perspective of the dynamics of integrable systems. After outlining and critically reviewing methods based on the inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a Gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operators we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density–density correlation functions. In both cases we observe a tendency toward the formation of crystal-like correlations at intermediate timescales