  We consider the time evolution of observables in the transverse field Ising
chain (TFIC) after a sudden quench of the magnetic field. We provide exact
analytical results for the asymptotic time and distance dependence of one- and
two-point correlation functions of the order parameter. We employ two
complementary approaches based on asymptotic evaluations of determinants and
form-factor sums. We prove that the stationary value of the two-point
correlation function is not thermal, but can be described by a generalized
Gibbs ensemble (GGE). The approach to the stationary state can also be
understood in terms of a GGE. We present a conjecture on how these results
generalize to particular quenches in other integrable models.
