The article presents a quantum kinetic framework to study interacting quan¬tum systems. Having the constituting model Hamiltonians of two-band semiconductor and the photoexcited electron-hole pair, their quantum kinetic evolution has been revi-sited. Solution to this nonlinear problem of electron-hole interaction is obtained making use of the self-consistency loop between the densities of photoexcited electrons and holes and the pairwise interaction terms in the constituting model Hamiltonians. In the leading order, this approach supports the required isomorphism between the pairwise interaction and the birth and annihilation operators of the photoexcited electrons and holes as a desirable property. The approach implies the Hilbert space and the tensor product mathematical techniques as an appropriate generalization of the noninteracting electron-hole pair toward several-body systems.
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