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We discuss stability and phase coherence of 1D trapped Bose gases and findthat inelastic decay processes, such as 3-body recombination, are suppressed inthe strongly interacting (Tonks-Girardeau) and intermediate regimes. This ispromising for achieving these regimes with a large number of particles."Fermionization" of the system reduces the phase coherence length, and at T=0the gas is fully phase coherent only deeply in the weakly interacting(Gross-Pitaevskii) regime.Comment: published versio

Stability and Phase Coherence of Trapped 1D Bose Gases