Random matrix line shape theory with applications to levy statistics

A model system of a bright state coupled to a manifold of dark states is analyzed with regard to the width distributions of the dark manifold induced in the bright state. Independent box shaped distributions are assumed for the energy distributions, the coupling distributions and the dark level width-distributions. The width distributions induced via the couplings from the dark levels into the bright state can be expressed in terms of Lévy functions in the limit of a sparse level density which relates to anomalous long-time relaxations of the state selected survival probabilities.