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 BEC regimes of a true condensate and quasicondensate, and the regime of a trapped gas of Tonks (gas of impenetrable bosons). The presence of a sharp cross-over to the BEC regime requires extremely small interaction between particles. We discuss how to distinguish between true and quasicondensates in phase coherence experiments. 
D.S. Petrov, G.V. Shlyapnikov, and J.T.M. Walraven