Scattering rates and lifetime of exact and boson excitons

TL;DR

This paper proves that treating excitons as bosons leads to fundamental inaccuracies in calculating their scattering rates and lifetimes, highlighting the importance of their composite nature.

Contribution

It demonstrates that bosonization cannot simultaneously accurately predict exciton scattering rates and lifetimes due to their composite nature.

Findings

A factor of 1/2 relates exciton lifetime and scattering rates.

Bosonization loses critical information about exciton composite structure.

Results challenge the validity of bosonization in interacting exciton problems.

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 $\tau_0$, correctly: A striking factor 1/2 exists between $\tau_0^{-1}$ 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.