  We investigate the relaxation dynamics of the integrable Lieb-Liniger model
of contact-interacting bosons in one dimension following a sudden quench of the
collisional interaction strength. The system is initially prepared in its
noninteracting ground state and the interaction strength is then abruptly
switched to a positive value, corresponding to repulsive interactions between
the bosons. We calculate equal-time correlation functions of the nonequilibrium
Bose field for small systems of up to five particles via symbolic evaluation of
coordinate Bethe-ansatz expressions for operator matrix elements between
Lieb-Liniger eigenstates. We characterize the relaxation of the system by
comparing the time-evolving correlation functions following the quench to the
equilibrium correlations predicted by the diagonal ensemble and relate the
behavior of these correlations to that of the quantum fidelity between the
many-body wave function and the initial state of the system. Our results for
the asymptotic scaling of local second-order correlations with increasing
interaction strength agree with the predictions of recent generalized
thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations
obtained within our approach exhibit a markedly different power-law dependence
on the interaction strength as the Tonks-Girardeau limit of infinitely strong
interactions is approached.
