Many-body fluctuations and the dynamics of liquid ⁴He

It has been firmly established that dynamic pair fluctuations make important contributions to medium- and short-wavelength behavior of the dynamic structure function of superfluid ⁴He. These fluctuations have, so far, been treated in the so-called "uniform limit approximation." In the first part of this work we show that the full solution of the equation of motion for pair fluctuations does not significantly change the results of the time-honored uniform limit approximation. However, pair fluctuations still fall significantly short of fully accounting for the medium-wavelength structure of the elementary excitation spectrum, i.e. the roton energy, and the energy of the short wavelength plateau seen in the dynamic structure function as measured by neutron scattering. Here we show how the inclusion of dynamic triplet fluctuations produces very satisfactory agreement with experiment. Insight into these results is obtained by examining them in terms of correlated Brillouin-Wigner perturbation theory just as it did for the physics of the contributions of pair fluctuations in previous work.