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We examine the possibility of Bose-Einstein condensation in one-dimensionalinteracting Bose gas subjected to confining potentials of the form $V_{\rmext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving theGross-Pitaevskii equation within the semi-classical two-fluid model. Thecondensate fraction, chemical potential, ground state energy, and specific heatof the system are calculated for various values of interaction strengths. Ourresults show that a significant fraction of the particles is in the lowestenergy state for finite number of particles at low temperature indicating aphase transition for weakly interacting systems.Comment: LaTeX, 6 pages, 8 figures, uses grafik.sty (included), to be  published in Phys. Rev.

Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials