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Using the adiabatic switching of interactions, we establish a condition forthe existence of electronic quasiparticles in a Luttinger liquid. It involves acharacteristic interaction strength proportional to the inverse square root ofthe system length. An investigation of the exact energy level separationprobability distribution shows that this interaction scale also corresponds toa cross-over from the non interacting behaviour to a rather typical case forintegrable systems, namely an exponential distribution. The level spacingstatistics of a spin $1/2$, one branch Luttinger model are also analyzed, aswell as the level statistics of a two coupled chain model.Comment: 22 pages, Late

Breakdown of the Fermi Liquid picture in one dimensional fermion systems: connection with the energy level statistics