Dynamic Susceptibility of the Free Fermi Gas in 2D

A detailed discussion of the dynamic susceptibility of the two dimensional free Fermi gas at zero and finite temperature is presented. The behaviour and evolution of the coherent and incoherent components of the dynamic structure function with the temperature and momentum transfer are analyzed. Particular attention is paid to the way in which their relative contribution changes with respect to the ~T=0 case. The influence of thermal effects on the lowest order sum rules of the coherent and incoherent responses is also discussed. Finally, similar analysis are presented for the real part of the dynamic susceptibility.