  We study the dynamics of a one-dimensional Bose gas after a sudden change of
the interaction strength from zero to a finite value using the numerical
time-evolving block decimation (TEBD) algorithm. It is shown that despite the
integrability of the system, local quantities such as the two-particle
correlation $g^{(2)}(x,x)$ attain steady state values in a short characteristic
time inversely proportional to the Tonks parameter $\gamma$ and the square of
the density. The asymptotic values are very close to those of a finite
temperature grand canonical ensemble with a local temperature corresponding to
initial energy and density. Non-local density-density correlations on the other
hand approach a steady state on a much larger time scale determined by the
finite propagation velocity of oscillatory correlation waves.
