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We present a general method, based on a multiple-scale approach, for derivingthe perturbative solutions of the scaling equations governing the expansion ofsuperfluid ultracold quantum gases released from elongated harmonic traps. Wediscuss how to treat the secular terms appearing in the usual naive expansionin the trap asymmetry parameter epsilon, and calculate the next-to-leadingcorrection for the asymptotic aspect ratio, with significant improvement overthe previous proposals.

Multiple-scale approach for the expansion scaling of superfluid quantum gases