Cooperative effects and photon localization in atomic gases: The two-dimensional case

We study photon escape rates from two-dimensional atomic gases while taking into account cooperative effects between the scatterers. Based on the spectrum of the random Euclidean matrix U-ij = J(0)(x(ij)), where x(ij) is the dimensionless random distance between any two atoms, a scaling behavior for the escape rates is obtained. This behavior is similar to the one obtained in the three-dimensional case, but qualitatively different from the result obtained in one dimension.