Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state

We derive a relationship between the optical conductivity scattering rate 1/\tau(\omega) and the electron-boson spectral function \alpha^2F(\Omega) valid for the case when the electronic density of states, N(\epsilon), cannot be taken as constant in the vicinity of the Fermi level. This relationship turned out to be useful for analyzing the experimental data in the pseudogap state of cuprate superconductors.