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Equilibration and Generalized GGE in the Lieb Liniger gas

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.