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Scattering rates and lifetime of exact and boson excitons

M. Combescot·O. Betbeder-Matibet
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Abstract

Although excitons are not exact bosons, they are commonly treated as such provided that their composite nature is included in effective scatterings dressed by exchange. We here \emph{prove} that, \emph{whatever these scatterings are}, they cannot give both the scattering rates $T_{ij}^{-1}$ and the exciton lifetime $τ_0$, correctly: A striking factor 1/2 exists between $τ_0^{-1}$ and the sum of $T_{ij}^{-1}$'s, which originates from the composite nature of excitons, irretrievably lost when they are bosonized. This result, which appears as very disturbing at first, casts major doubts on bosonization for problems dealing with \emph{interacting} excitons.

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M. Combescot, O. Betbeder-Matibet. 2004-05-17. Scattering rates and lifetime of exact and boson excitons. https://doi.org/10.1103/physrevlett.93.016403

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