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 consider generic, or ''dirty'' (surrounded by matter), stationary rotating black holes with axial symmetry. The restrictions are found on the asymptotic form of metric in the vicinity of nonextremal, extremal and ultraextremal horizons, imposed by the conditions of regularity of increasing strength: boundedness on the horizon of the Ricci scalar, of scalar quadratic curvature invariants, and of the components of the curvature tensor in the tetrad attached to a falling observer. We show, in particular, that boundedness of the Ricci scalar implies the ''rigidity'' of the horizon's rotation in all cases, while the finiteness of quadratic invariants leads to the constancy of the surface gravity. We discuss the role of quasiglobal coordinate r that is emphasized by the conditions of regularity. Further restrictions on the metric are formulated in terms of subsequent coefficients of expansion of metric functions by r. The boundedness of the tetrad components of curvature tensor for an observer crossing the horizon is shown to lead in the horizon limit to diagonalization of the Einstein tensor in the frame of a zero angular momentum observer on a circular orbit (ZAMO frame) for horizons of all degrees of extremality.

We consider collision of two massive particles in the equatorial plane of an axially symmetric stationary spacetime that produces two massless particles afterwards. It is implied that the horizon is absent but there is a naked singularity or another potential barrier that makes possible the head-on collision. The relationship between the energy in the center of mass frame E c.m. and the Killing energy E measured at infinity is analyzed. It follows immediately from the Wald inequalities that unbounded E is possible for unbounded E c.m. only. This can be realized if the spacetime is close to the threshold of the horizon formation. Different types of spacetimes (black holes, naked singularities, wormholes) correspond to different possible relations between E c.m. and E. We develop a general approach that enables us to describe the collision process in the frames of the stationary observer and ZAMO (zero angular momentum observer). The escape cone and escape fraction are derived. A simple explanation of the existence of the bright spot is given. For the particular case of the Kerr metric, our results agree with the previous ones found in M. Patil, T. Harada, K. Nakao, P.S. Joshi, and M. Kimura, Phys. Rev. D 93, 104015 (2016