  The Stokes and anti-Stokes components in the inelastic scattering of light
are related to phonon statistics and have been broadly used to measure
temperature and phonon lifetimes in different materials. However, correlation
between the components are expected to change the Stokes/anti-Stokes intensity
ratio, imposing corrections to the broadly used Bose-Einstein statistics. Here
the excitation power dependence of these scattering processes is theoretically
described by an effective Hamiltonian that includes correlation between the
Stokes and the anti-Stokes events. The model is used to fit available
experimental results in three-dimensional diamond and two-dimensional graphene,
showing that the phenomenon can significantly increase in the low-dimensional
system under specific resonance conditions. By setting the scientific basis for
the Stokes-anti-Stokes correlated phenomenon, the use of the Bose-Einstein
population function for reasoning the inelastic scattering is generalized,
providing a model to predict the conversion of optical phonons into heat or
light, according to coupling constants and decay rates. The model applies to
inelastic scattering in general.
