High- and low-frequency behavior of response functions in a Bose condensed liquid

Recent studies of superfluid ⁴He have shown that it is useful to separate S(Q, ) into condensate and regular parts. We discuss the f-sum rule and the compressibility sum rule which the condensate part satisfies at T = 0K and at finite temperatures. Our work is based on the microscopic approach of Gavoret and Nozières, as amended by Nepomnyashchii and Nepomnyashchii. We also discuss the implications of the Wong-Gould sum rule for the condensate part of S(Q, ).This research was supported by a grant from NSERC, Canada.