Order Parameter at the Boundary of a Trapped Bose Gas

Abstract

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 $a_{{}_{HO}}$, follows the law $E_{kin}/N\propto R^{-2}[\log (R/a_{{}_{HO}})+const.]$, 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.

11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

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• Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas
• Bosons in anisotropic traps: ground state and vortices
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