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We consider in dimension 3 a homogeneous superfluid at very low temperature T having two types of excitations, (i) gapless acoustic phonons with a linear dispersion relation at low wave number, and (ii) gapped ° quasiparticleswith a quadratic (massive) dispersion relation in the vicinity of its extrema. Recent works [Nicolis and Penco (2018), Castin, Sinatra and Kurkjian (2017, 2019)], extending the historical study by Landau and Khalatnikov on the phonon-roton interaction in liquid helium 4, have explicitly determined the scattering amplitude of a thermal phonon on a ° quasiparticle at rest to leading order in temperature. We generalize this calculation to the case of a ° quasiparticle of arbitrary subsonic group velocity, with a rigorous construction of the S matrix between exact asymptotic states, taking into account the unceasing phonon-phonon and phonon-° interaction, which dresses the incoming and emerging phonon and ° quasiparticle by virtual phonons; this sheds new light on the Feynman diagrams of phonon-° scattering. In thewhole domain of the parameter space (wave number k, interaction strength, etc.) where the ° quasiparticle is energetically stable with respect to the emission of phonons of arbitrary wavevector, we can therefore characterize the erratic motion it performs in the superfluid due to its unceasing collisions with thermal phonons, through (a) the mean force F(k) and (b) longitudinal and transverse momentum diffusion coefficients D(k) and D?(k) coming into play in a Fokker-Planck equation, then, at long times when the quasiparticle has thermalized, (c) the spatial diffusion coefficient Dspa, independent of k. At the location k0 of an extremum of the dispersion relation, where the group velocity of the quasiparticle vanishes, F(k) varies linearly with velocity with an isotropic viscous friction coefficient ® that we calculate; if k0 Æ 0, the momentum diffusion is also isotropic and F(k0) Æ 0; if k0 È 0, it is not (D(k0) 6Æ D?(k0)), and F(k0) is non-zero but subleading with respect to ® by one order in temperature. The velocity time correlation function, whose integral gives Dspa, also distinguishes between these two cases (k0 is now the location of the minimum): if k0 Æ 0, it decreases exponentially, with the expected viscous damping rate of the mean velocity; if k0 È 0, it is bimodal and has a second component, with an amplitude lower by a factor/T, but with a lower damping rate in the same ratio (it is the thermalization rate of the velocity direction); this balances that. We also characterize analytically the behavior of the force and of the momentumdiffusion in the vicinity of any sonic edge of the stability domain where the quasiparticle speed tends to the speed of sound in the superfluid. The general expressions given in this work are supposedly exact to leading order in temperature (order T 8 for F(k), order T 9 for D(k), D?(k) and F(k0), order T ¡7 for Dspa). They however require an exact knowledge of the dispersion relation of the ° quasiparticle and of the equation of state of the superfluid at zero temperature. We therefore illustrate them in the BCS approximation, after calculating the stability domain, for a fermionic ° quasiparticle (an unpaired fermion) in a superfluid of unpolarized spin 1/2 fermions, a system that can be realised with cold atoms in flat bottom traps; this domain also exhibits an interesting, unobserved first order subsonic instability line where the quasi-particle is destabilized by emission of phonons of finite wave vectors, in addition to the expected sonic instability line resulting from Landau's criterion. By the way, we refute the thesis of Lerch, Bartosch and Kopietz (2008), stating that there would be no fermionic quasiparticle in such a superfluid. [ABSTRACT FROM AUTHOR]

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La dualité d'un champ le fait apparaître, à une date donnée, sous l'aspect spatial d'une onde; ou bien, en un point donné, sous l'aspect temporel d'un signal. On adopte un critère réaliste ouvrant une détermination expérimentale précise d'un repère de position spatiale de l'onde en milieu dispersif; ou encore du temps d'arrivée du signal. Dans la progression de ces repères s'introduit spontanément, en parallèle avec la vitesse de phase, une vitesse de groupe U dont l'expression est celle de la vitesse de groupe/signal du paquet d'ondes traditionnel. Ces deux grandeurs sont caractéristiques du seul milieu de transmission. A l'onde progressive, correspond alors une certaine vitesse d'onde, qui est la moyenne de l'opérateur U dans un état lié à la structure de l'onde origine de référence. Au signal perçu par un capteur fixe, correspond une vitesse différente: la vitesse de signal, inverse de la moyenne de l'opérateur U dans un état lié à la structure du signal d'émission. Vitesse d'onde et vitesse de signal dépendent ainsi, non seulement du milieu, mais aussi de la forme du signal d'émission. Toutes deux s'identifient cependant à la vitesse de groupe U dans le cas particulier d'un spectre très étroit: on rejoint ici le paquet d'ondes classique. La vitesse de groupe s'avère alors comme la vitesse du repère lié à l'amplitude complexe du signal analytique progressif; parallèlement à la célérité de sa porteuse, la vitesse de phase. Cette approche permet de décrire l'allure de la déformation d'une onde progressive en milieu dispersif et de la relier, par analogie, à la diffraction de Fresnel. La prise en compte de l'affaiblissement associé à la dispersion conserve globalement les mêmes propriétés, en dehors des zones anormales. A radiated field always appears in a dual, spatial and temporal, aspect. Its spatial one is the wave the author would observe at a given time. Its temporal one is the signal he receives at a given point. The aim of this paper is then to determine bulk velocities of both signal and wave - without any limiting assumption on their spectral widths - in case the field is being radiated thru a dispersive medium. A realistic criterion is first adopted that enables an accurate measurement of the instant position of the wave, by means of a definite space-marker (the wave center,). The same criterion also leads to a similar time-marker (the signal center,) that will be used in measuring the receiving time of the signal. By studying the motion of these markers an operator U spontaneously appears beside the phase velocity. This operator has the same analytical expression as the usual group/signal velocity of a wave packet. Therefore U should be also called group velocity. Both group and phase velocities depend on the transmitting medium only. To the travelling wave then corresponds an uniform motion of its wave center, with some wave velocity. The latter consists of the mean of operator U in a state which is associated with the wave structure at the time origin. To the signal, when received by a fixed transductor, also corresponds some signal velocity. Its value is the inverse of the mean of operator U in a state which is associated with the signal structure at the transmitter. Thus, wave velocity and signal velocity not only depend on the transmitting medium, but depend on the emitted signal form too. However both of them become identified with the group velocity U in the particular case of a very narrow spectrum. Thus agreeing with the usual wave packet. In such a case the group velocity turns out to be the velocity of the very marker that belongs to the amplitude of the transmitted analytic signal. Such an approach also enables us to describe signal distortion in a dispersive medium. By analogy, it leads to relating that distortion to Fresnel diffraction. Outside anomalous zones, the above properties are roughly maintened when attenuation is taken into account in relation to dispersion. [ABSTRACT FROM AUTHOR]