Dynamical structure factor of a one-dimensional harmonic liquid: Comparison of different approximation methods

The optical properties of Anderson-localized many-particle excitations in doped crystals are discussed assuming that the direct interaction between the active ions is greater than their interaction with the radiation field. It is shown that in this case the Anderson localization of the excitation energy on a finite number of ions has no influence in zeroth order on the absorption and emission properties at low excitation intensities used in conventional spectroscopy. Only at higher excitation intensities resulting in multiply excited many-ion states are characteristic quenching effects of the luminescence expected. These become evident by a conversion of the multiply excited states into fast relaxing, degenerate states either of the ions themselves or of the host lattice. These quenching effects offer possibilities to determine experimentally the number of coherently coupled ions forming the many-particle Anderson-localized excitations.