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Order Parameter at the Boundary of a Trapped Bose Gas

F. Dalfovo·L. Pitaevskii·S. Stringari
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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 $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, 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.

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F. Dalfovo, L. Pitaevskii, S. Stringari. 1996-04-11. Order Parameter at the Boundary of a Trapped Bose Gas. https://doi.org/10.1103/physreva.54.4213

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