Self-organization in dissipative optical lattices

We show that the transition from Gaussian to the q-Gaussian distributions occurring in atomic transport in dissipative optical lattices can be interpreted as self-organization by recourse to a modified version of Klimontovich's S-theorem. As a result, we find that self-organization is possible in the transition regime, only where the second moment << p(2)>> is finite. Therefore, the nonadditivity parameter q is confined within the range 1 < q < 53, although the whole spectrum of q values, i.e., 1 < q < 3, is considered theoretically possible. The range of q values obtained from the modified S-theorem is also confirmed by the experiments carried out by Douglas [Phys. Rev. Lett. 96, 110601 (2006)].