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Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory., Comment: 5 pages, 3 figures, submitted to Phys. Rev. Lett

Texto completo: arXiv:1007.4664v1, We use a recently developed order parameter expansion method to study the transition to synchronous firing occurring in a system of coupled active rotators under the exclusive presence of quenched noise. The method predicts correctly the existence of a transition from a rest state to a regime of synchronous firing and another transition out of it as the intensity of the quenched noise increases and leads to analytical expressions for the critical noise intensities in the large coupling regime. It also predicts the order of the transitions for different probability distribution functions of the quenched variables. Using numerical simulations and finite-size scaling theory to estimate the critical exponents of the transitions, we found values which are consistent with those reported in other scalar systems in the exclusive presence of additive static disorder., We thank Luis F. Lafuerza and Lucas Lacasa for fruitful discussions. We acknowledge financial support from the EU NoE BioSim, LSHB-CT-2004-005137, and project FIS2007-60327 from MEC (Spain). NK is supported by a grant from the Govern Balear.