Asymptotic symmetries in an optical lattice

It was recently remarked by Lutz [Phys. Rev. A 67, 051402(R) (2003)] that the equation for the marginal Wigner distribution in an optical lattice admits a scale-free distribution corresponding to Tsallis statistics. Here we show that this distribution is invariant under an asymptotic symmetry of the equation and hence that this scale-free behavior can be understood in terms of symmetry analysis.