[en] The authors discuss a natural generalization of the uncertainty inequality holding in the case of non-hermitian operators. The inequality is employed to derive useful constraints on the behavior of quantum fluctuations in problems with continuous-group symmetries. Applications to Bose superfluids, antiferromagnets, and crystals at zero temperature are discussed. In particular, a simple and direct proof is provided of the absence of long-range order at zero temperature in the 1D case. A new inequality involving the spectral function at finite temperature is finally derived

[en] We study the role of the virtual emission of rotons by ripplons near the threshold Δ at zero temperature. We suggest that the ripplon dispersion curve should remain below this threshold as a consequence of the ripplon-roton hybridization. A simple hydrodynamic description is used to provide a quantitative estimate of the ripplon dispersion curve

[en] We study the response of Bose ⁴He clusters to an external field corresponding to a rotation with frequency ω. An explicit form for the normal (nonsuperfluid) fraction of the system as a function of the temperature T and of the mass number N of the cluster is obtained under the assumption that only surface modes are thermally excited. The critical behaviour of ⁴He clusters at high rotational frequencies is also investigated. (orig.)

[en] We discuss the effects of a weak random external potential on the properties of the dilute Bose gas at zero temperature. The results recently obtained by Huang and Meng for the depletion of the condensate and of the superfluid density are recovered. Results for the shift of the velocity of sound as well as for its damping due to collisions with the external field are presented. The damping of phonons is calculated also for dense superfluids

No abstract available

[en] The roton contribution to the temperature dependence of the condensate density is discussed. The analysis is carried out through the inclusion of a gauge symmetry breaking field. Under the hypothesis that the thermal excitation of rotons is the main responsible for the depletion of the condensate, the authors obtain an explicit result for the temperature dependence of the condensate density which rather well agrees with the available experimental data. 11 refs., 1 fig

[en] This paper is devoted to the calculation of the momentum of localized excitations, such as solitons and vortex rings, moving in a superfluid. The direct calculation of the momentum by integration of the mass flux density results in a badly-converging integral. I suggest a method for the renormalization of the integral with the explicit separation of a term related to the vortex line. This term can be calculated explicitly and gives the main contribution for the rings whose size is large compared to the healing length. I compare my method with the Jones and Roberts prescription for renormalization. I investigate the case of a uniform superfluid, and that of a superfluid in a cylindrical trap. I discuss the calculation of the jump in the phase of the order parameter and obtain a simple estimate for this jump

[en] It is shown that the Raabe and Welsch [Phys. Rev. A 71, 013814 (2005)] criticism of the Dzyaloshinskii-Lifshitz-Pitaevskii theory of the van der Waals-Casimir forces inside a medium is based on misunderstandings. It is explained why and at which conditions one can use the ''Minkowski-like'' stress tensor for calculations of the forces. The reason why, in my opinion, the approach of Raabe and Welsch is incorrect is discussed

[en] A variety of solitary waves, such as solitons, vortex rings, solitonic vortices, and more complex entities, have recently been predicted to exist. They can move in superfluid ultracold gases along elongated traps. The theoretical description of this motion requires knowledge of the inertial soliton mass and the effective number of particles in it as functions of the soliton energy. While these functions can be calculated by a microscopic theory, it is also possible to express them directly in terms of observable quantities, such as the order parameter phase jump and the particle number deficiency in the soliton. In this article, the corresponding equations are derived in a simple and physically clear way and applied to the recently predicted ‘magnetic soliton’ in mixtures of Bose gases in various spin states. (methodological notes)

[en] A new theory describing the interaction between atoms and a conductor with small densities of current carriers is presented. The theory takes into account the penetration of the static component of the thermally fluctuating field in the conductor and generalizes the Lifshitz theory in the presence of a spatial dispersion. The equation obtained for the force describes the continuous crossover between the Lifshitz results for dielectrics and metals