Exact calculation of distributions for excitonic oscillator strength and inverse participation ratio in disordered quantum wires

We investigate the optical spectra and localization properties of excitons in disordered quantum wires within the Anderson model. The exact distributions of the oscillator strength and the inverse participation ratio are obtained by an extension of work by Bertrand Halperin [Phys. Rev. 139, A104 (1965)]. The results are confirmed by numerical simulations. Approximate expressions valid in limiting cases are critically discussed. Semiquantitative agreement with experimental oscillator strength distributions derived from available optical near-field spectra of semiconductor quantum wires is found.