Euclidean matrix theory of random lasing in a cloud of cold atoms

We develop an ab initio analytic theory of random lasing in an ensemble of atoms that both scatter and amplify light. The theory applies all the way from low to high density of atoms. The properties of the random laser are controlled by an Euclidean matrix with elements equal to the Green's function of the Helmholtz equation between pairs of atoms in the system. Lasing threshold and the intensity of laser emission are calculated in the semiclassical approximation. The results are compared to the outcome of the diffusion theory of random lasing.Comment: 6 pages, 4 figure

Absence of bimodal peak spacing distribution in the Coulomb blockade regime

Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in agreement with the experimental observations. We attribute this behavior to the tendency of an even number of electrons to gain on-site interaction energy by removing the spin degeneracy. Thus, the dot is predicted to show a non trivial electron number dependent spin polarization. Experimental test of this hypothesis based on the spin polarization measurements are proposed.Comment: 13 pages, 3 figures, accepted for publication in PRL - a few small change