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Many-body effects are known to play a crucial role in the electronic andoptical properties of solids and nano-structures. Nevertheless the majority oftheoretical and numerical approaches able to capture the influence of Coulombcorrelations are restricted to the linear response regime. In this work weintroduce a novel approach based on a real-time solution of the electronicdynamics.The proposed approach reduces to the well-known Bethe-Salpeterequation in the linear limit regime and it makes possible, at the same time, toinvestigate correlation effects in nonlinear phenomena. We show the flexibilityand numerical stability of the proposed approach by calculating the dielectricconstants and the effect of a strong pulse excitation in bulk {\it h}-BN.

A real-time approach to the optical properties of solids and nano-structures: the time-dependent Bethe-Salpeter equation