Application of the theory of continuous media to the description of thermal excitations in superfluid helium

We propose a model for the quasiparticles of superfluid ⁴He which describes both phonons and rotons in a unified way. The theory is based on the fact that the thermal de Broglie wavelengths of the atoms overlap each other. This allows us to treat superfluid ⁴He as a continuous medium at all length scales. Then the parameters of the continouous medium (density, pressure, and velocity) can be given a probabilistic value at each point in space. The quasiparticles of superfluid ⁴He are small fluctuations in these parameters; the frequency and wave vector of a fluctuation correspond to the energy and momentum of the quasiparticle, respectively. Using the Lagrange formalism we derive equations for the potential associated with these fluctuations, and this leads to a generalized wave equation. From the Hamiltonian formalism we derive a system of equations for the variables of a continuous medium, and show that in the general case there is a non-local dependence between pressure and density. Applying the methods of the mechanics of continuous media, we calculate the creation probabilities for both phonons and rotons by phonons in a solid, in a unified way. This theory explains why R^- rotons are not created by a heater. The theory is compared with those of others, and the results with experiments.