Specific heat of interacting Bose systems at low temperatures

The constant-volume specific heat CV of Bose liquids at low temperature T is investigated using a microscopic generalization of the dynamical quasiparticle model introduced by Landau. The utility of the dynamical quasiparticle model, which is to be distinguished from the statistical quasiparticle model, is based on the outstanding feature of Bose liquids that the single-particle spectrum and the density spectrum coincide. Contributions from collective modes not included in the dynamical quasiparticle model are estimated to be negligible at low T. An exact expression is derived for the leading lifetime contribution δCV due to the damping of the phonon and δCV is found to be second order in Γ, the imaginary part of the matrix self-energy. An explicit microscopic calculation of δCV is performed for a one-parameter Bose gas in a perturbation approximation that includes three-phonon processes and satisfies the general symmetry requirements for Bose systems. The surprising result is that δCV~T⁵lnT. The application of this result to superfluid ⁴He is discussed. It is concluded that the leading phonon dispersion cannot be rigorously determined from a measurement of the O(T⁵) term of CV.