Analytic representation of a zero-frequency transport coefficient. General theory and application to ultrasonic attenuation in CsNiCl3

Starting from Mori's continued-fraction representation of spectral functions, we derive an analytical formula for a transport coefficient in the static limit. The formula then is applied to the phonon dynamics of a model Hamiltonian for a compressible one-dimensional magnetic system. The resulting expression for the ultrasonic attenuation coefficient is compared with an experiment for CsNi${\mathrm{Cl}}_3$. Good qualitative agreement is obtained.