Phonon-Phonon Interactions in Liquid Helium II

The quantum hydrodynamics of Landau is here regarded as a means of calculating phonon-phonon interactions in liquid helium II. This theory is tested by applying it to the low-density Bose-Einstein gas, at low temperatures and long wavelengths, it agrees with the microscopic theory of the Bose-Einstein gas. This agreement justifies the past use of the hydrodynamic theory to calculate the Landau-Rumer sound absorption in liquid helium; however, the calculated absorption is roughly half that measured by Abraham, Eckstein, Ketterson, Kuchnir, and Vignos. Hence the higher-order terms in the hydrodynamic theory are considered; they probably cannot account for the discrepancy.