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Bethe-Salpeter Equation and Excitonic effects: a short introduction Valerio Olevano Laboratoire des Solides Irradiés École Polytechnique, Palaiseau

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Exciton and Bethe-Salpeter equation c v cv h c v h c v h W EXC P = ++ O(2) + RPAGWBSE Polarisation e-e- h+h+

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Definitions L = 2-particles Correlation Function Polarization Dielectric Function (observables) G = Green Function 2-particles Green Function

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Bethe-Salpeter Equation Bethe-Salpeter Equation Interaction Kernel = Self-Energy W =Screened Interaction

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Resolution of the BSE: Excitonic Hamiltonian Overlap Matrix Excitonic Eigenfunctions Excitonic Eigenvalues Excitonic Hamiltonian

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Excitonic Macroscopic Dielectric Function

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Excitonic Hamiltonian: Resonant and Coupling terms Hermitean Symmetric full diago of a Non-Hermitean matrix or diagonalization of an Hermitean matrix (R) plus (eventually) Perturbation Theory

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