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We use the coordinate Bethe ansatz to exactly calculate matrix elementsbetween eigenstates of the Lieb-Liniger model of one-dimensional bosonsinteracting via a two-body delta-potential. We investigate the staticcorrelation functions of the zero-temperature ground state and their dependenceon interaction strength, and analyze the effects of system size in thecrossover from few-body to mesoscopic regimes for up to seven particles. Wealso obtain time-dependent nonequilibrium correlation functions for fiveparticles following quenches of the interaction strength from two distinctinitial states. One quench is from the non-interacting ground state and theother from a correlated ground state near the strongly interactingTonks-Girardeau regime. The final interaction strength and conserved energy arechosen to be the same for both quenches. The integrability of the model highlyconstrains its dynamics, and we demonstrate that the time-averaged correlationfunctions following quenches from these two distinct initial conditions areboth nonthermal and moreover distinct from one another.

A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas