We generalize the fully renormalized kinetic-theory formalism of Mazenko to normal quantum fluids and show that the Kubo linear-response function satisfies a generalized kinetic equation with a memory function or kernel nonlocal in space and time. In contrast to classical systems, the generalized kinetic equations must be supplemented by a "boundary-condition" equation for the static part of the response function. The memory function is separated in a natural way into a static and dynamic part; only the static part appears in the boundary-condition equation. We consider a normal Fermi liquid at low temperatures and obtain the correspondence, in the limit of small wave vector k and small frequency ω, between the formal expressions for the memory function and the phenomenological Landau theory. From this analysis and the use of kinetic modeling we develop a simple model for the memory function which is applicable to higher k and ω, includes collisional effects, and is consistent with the conservation laws. The dynamic-structure function S(k, ω) is obtained from the generalized kinetic equation and evaluated for liquid He3 at low temperatures using the effective mass, the static-structure function, and the viscosity as input. The model results for S(k, ω) and the dispersion relation of zero sound contain no free parameters and are consistent with recent inelastic-neutron-scattering measurements on liquid He3.
Bibliographical noteFunding Information:
Work supported in part by NSF Grant No. DMR 76-21298, the Materials Research Laboratory of the NSF, and the Louis Block Fund of the University of Chicago.