Interpolation between spectra satisfying sum rules

A method is presented which is able to interpolate between spectra depending parametrically on one variable and obeying a sum rule. This enables the description of experiments with a finite resolution in that parameter because integrals over certain parameter ranges are easily obtained, as for instance in the case of inelastic x-ray scattering with finite resolution in momentum transfer. Beyond the sum rule, the method does not use further assumptions about the physics of the system. It is applicable to a wide range of spectra as for instance the dynamic structure factor or the dielectric function for different moduli or directions of momentum transfer, absorption spectra for different alloy compositions or for a range of nanocrystal sizes, probability distributions, etc. The method is expected to be useful not only in the simulation of experimental spectra but also in calculations where the determination of certain spectral quantities is numerically cumbersome. A code carrying out the interpolation is provided.