Order parameter at the boundary of a trapped Bose gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius R and of the harmonic oscillator length ${\mathit{a}}_{\mathrm{HO}}$, follows the law ${\mathit{E}}_{\mathrm{kin}}$/N\ensuremath{\propto}${\mathit{R}}^{\mathrm{\ensuremath{-}}2}$[ln(R/${\mathit{a}}_{\mathrm{HO}}$)+ const], approaching, for large R, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed. \textcopyright{} 1996 The American Physical Society.

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