The Luttinger model following a sudden interaction switch-on

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The evolution of correlations in the exactly solvable Luttinger model (a model of interacting fermions in one dimension) after a sudden interaction switch-on is analytically studied. When the model is defined on a finite-size ring, zero-temperature correlations are periodic in time. However, in the thermodynamic limit, the system relaxes algebraically towards a stationary state which is well described, at least for some simple correlation functions, by the generalized Gibbs ensemble recently introduced by Rigol et al. [cond-mat/0604476]. The critical exponent that characterizes the decay of the one-particle correlation function is different from the known equilibrium exponents. Experiments for which these results can be relevant are also discussed.