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In this paper we study nonequilibrium dynamics of one dimensional Bose gasfrom the general perspective of dynamics of integrable systems. After outliningand critically reviewing methods based on inverse scattering transform,intertwining operators, q-deformed objects, and extended dynamical conformalsymmetry, we focus on the form-factor based approach. Motivated by possibleapplications in nonlinear quantum optics and experiments with ultracold atoms,we concentrate on the regime of strong repulsive interactions. We considerdynamical evolution starting from two initial states: a condensate of particlesin a state with zero momentum and a condensate of particles in a gaussianwavepacket in real space. Combining the form-factor approach with the method ofintertwining operator we develop a numerical procedure which allows explicitsummation over intermediate states and analysis of the time evolution ofnon-local density-density correlation functions. In both cases we observe atendency toward formation of crystal-like correlations at intermediate timescales.

journal of statistical mechanics

Exact methods in analysis of nonequilibrium dynamics of integrable  models: application to the study of correlation functions in nonequilibrium  1D Bose gas