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We propose a model for the quasiparticles of superfluid 4 He 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 4 He as a continuous medium at all length scales. Then the parameters of the continouous medium ͑density, pressure, and velocity͒ can be given a probabilistic value at each point in space. The quasiparticles of superfluid 4 He 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 Ϫ rotons are not created by a heater. The theory is compared with those of others, and the results with experiments.

HeII quasiparticles with the interface: their transmission, reflection and conversion into each other. These are the fundamental elementary processes that determine the heat exchange between HeII and a solid, and the associated phenomena, such as the Kapitza temperature jump (see for example [11]). We investigate all these phenomena. The probability of creation of each quasiparticle at the interface is derived for all cases. The failures of attempts to detect R − rotons prior to experiments [3] is explained, and predictions are made for new experiments on the interaction of phonons and rotons with a solid and the creation of R − rotons at the interface by high energy phonons (h-phonons). arXiv:1206.3678v1 [cond-mat.other]

We have carried out a theoretical investigation of the experimentally observed phenomenon that long-lived high-energy ͑h͒ phonons are generated by a moving cloud of low-energy ͑l͒ phonons. The h phonons are created from the l phonons by four phonon processes (4pp) and they are lost from the trailing edge of the l phonon cloud, because they have a lower velocity than the l phonons, and form the h phonon cloud. We obtain a set of equations which completely describe these phenomenon. The solution of these equations accounts for the high efficiency of the conversion process: a major part of the energy in the l phonons can be converted to h phonons within the propagation time of the pulse (Ͻ10 Ϫ4 s). In short pulses (Ͻ10 Ϫ7 s) the h phonons escape as soon they are created, but in long pulses the h phonon density increases within the l cloud. It is shown that in long phonon pulses there can be a suprathermal number of h phonons within the l cloud. The theory describes the cooling of pulses of different length due to energy being transformed into h phonons. It also accounts well for the important characteristics of h phonon generation which is an unusual example of energy transferring from low-energy to high-energy states.

There exists a transverse sound mode in superfluid helium, in addition to the first and second sound modes. In this mode, the velocity of the normal component oscillates in the direction perpendicular to the wave vector; hence, it is named the transverse mode. We analyze this mode at arbitrary values of the relative velocity of the normal and superfluid components. In general, temperature, pressure, and superfluid velocity also oscillate. The general relations between the amplitudes of the oscillating variables in the transverse mode are found in a general direction of the wave vector with respect to the relative velocity of the normal fluid and superfluid. We estimate the attenuation of the transverse mode in phonon pulses and discuss the possibility of detecting it experimentally.