Regimes of quantum degeneracy in trapped 1D gases

We discuss the regimes of quantum degeneracy in a trapped 1D gas and obtain the diagram of states. Three regimes have been identified: the Bose-Einste in condensation (BEC) regimes of a true condensate and quasicondensate, and the regime of a trapped Tonks gas (gas of impenetrable bosons). The presen ce of a sharp crossover to the BEC regime requires extremely small interact ion between particles. We discuss how to distinguish between true and quasi condensates in phase coherence experiments.