Order Parameter at the Boundary of a Trapped Bose Gas

TL;DR

This paper derives an explicit boundary solution for the order parameter of a trapped Bose gas using an expansion of the Gross-Pitaevskii equation, revealing kinetic energy scaling and discussing Josephson currents in double traps.

Contribution

It provides a new analytical approach to the boundary behavior of a trapped Bose gas and explores Josephson effects in double trap potentials.

Findings

Kinetic energy scales as R^{-2} with a logarithmic correction.

Explicit boundary order parameter solution derived.

Discussion of Josephson current in double traps.

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.