Finite Temperature Dynamic Structure Function of the Free Fermi Gas

A detailed discussion of the coherent and incoherent dynamic structure function of the free Fermi gas at finite temperature is presented. Their behavior and evolution with the momentum transfer and the temperature is analyzed, while particular attention is paid to the way in which their relative contribution changes with respect to the $\tilde{T}=0$ case. The influence of thermal effects on the lowest order sum rules of the coherent and incoherent responses is also discussed. Finally, the scaling properties of the responses at high momentum transfer as a function of the temperature are also analyzed.