  We study the nonequilibrium properties of the one dimensional Lieb Liniger
model in the finite repulsion regime. Introducing a new version of the Yudson
representation applicable to finite size systems and appropriately taking the
infinite volume limit we are able to study equilibration of the Lieb Liniger
gas in the thermodynamic limit. We provide a formalism to compute various
correlation functions for highly non equilibrium initial states. We are able to
find explicit analytic expressions for the long time limit of the expectation
of the density, density density and related correlation functions. We show that
the gas equilibriates to a diagonal ensemble which we show is equivalent to a
generalized version of the GGE for sufficiently simple correlation functions,
which in particular include density correlations.
