Finite temperature dynamic structure function of the free Bose gas

A detailed calculation of the finite temperature dynamic structure function of the free Bose gas is presented and discussed. After a short derivation of the expressions describing the exact response S(q, omega; T) and the imp ulse approximation (IA) S-IA(q, omega; t), their main properties and their evolution with q and T are analyzed. The lowest order energy weighted sum r ules of both S(q, omega; T) and S-IA(q, omega; T) are also derived and comm ented. Finally, the q --> infinity asymptotic behavior is analyzed and disc ussed in terms of scaling laws. (C) 2000 Elsevier Science B.V. All rights r eserved.