Generalized semiconductor Bloch equations: Local fields and transient gratings

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Abstract
Equations of motion for two-point equal-time electronic correlation functions, which describe near-resonant optical excitation of semiconductors in the Hartree approximation, are derived. These equations generalize the common semiconductor Bloch equations to incorporate inhomogeneous excitation of the medium and strong dielectric effects. We show that the many-body effects on the optical nonlinearity cannot be fully included by simply replacing the external electric field by the local field.