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

Many-body effects are known to play a crucial role in the electronic and optical properties of solids and nano-structures. Nevertheless the majority of theoretical and numerical approaches able to capture the influence of Coulomb correlations are restricted to the linear response regime. In this work we introduce a novel approach based on a real-time solution of the electronic dynamics.The proposed approach reduces to the well-known Bethe-Salpeter equation in the linear limit regime and it makes possible, at the same time, to investigate correlation effects in nonlinear phenomena. We show the flexibility and numerical stability of the proposed approach by calculating the dielectric constants and the effect of a strong pulse excitation in bulk {\it h}-BN.