Dissipative Coefficients of Superfluid Helium

The linearized hydrodynamic equations for superfluid ${\mathrm{He}}^4$ are derived starting from the kinetic equations of Khalatnikov. Only the lowest-order dissipative terms are considered. The Boltzmann equation for the phonons and rotons is solved formally by expanding the distribution function in terms of the eigenfunctions of the linearized collision operator. The resulting hydrodynamic equations contain dissipative terms of the form proposed by Landau and Khalatnikov. Formal expressions are given for the viscosities and the thermal kinetic coefficient. Finally, relations which may hold between the dissipative coefficients when the collision operator has special properties are discussed.