The temperature dependence of the optical line width of an impurity em
bedded in a glass matrix is investigated. A model Hamiltonian which co
uples the impurity to the characteristic soft modes of the glasses in
the phonon field of the matrix is introduced. We find an excellent agr
eement between our model predictions and experimental data. We are als
o able to reproduce supralinear behaviors in low-temperature regime wi
thout any adjustable parameter for the density of states. Finally, the
quadratic behavior extending to very low temperatures is explained in
terms of the Bose Peak equivalent temperature.