This report deals with the quantum field theory of particle oscillations in vacuum. We first review the various controversies regarding quantum-mechanical derivations of the oscillation formula, as well as the different field-theoretical approaches proposed to settle them. We then clear up the contradictions between the existing field-theoretical treatments by a thorough study of the external wave packet model. In particular, we show that the latter includes stationary models as a subcase. In addition, we explicitly compute decoherence terms, which destroy interferences, in order to prove that the coherence length can be increased without bound by more accurate energy measurements. We show that decoherence originates not only in the width and in the separation of wave packets, but also in their spreading through space-time. In this review, we neither assume the relativistic limit nor the stability of oscillating particles, so that the oscillation formula derived with field-theoretical methods can be applied not only to neutrinos but also to neutral K and B mesons. Finally, we discuss oscillations of correlated particles in the same framework.Comment: v2, 124 pages, 10 figures (7 more); updated review of the literature; complete derivation of the oscillation probability at short and large distance; more details on the influence of the spreading of the amplitude on decoherence; submitted to Physics Report

Enceladus's gravity and shape have been explained in terms of a thick isostatic ice shell floating on a global ocean, in contradiction of the thin shell implied by librations. Here we propose a new isostatic model minimizing crustal deviatoric stress and demonstrate that gravity and shape data predict a 38 ± 4 km thick ocean beneath a 23 ± 4 km thick shell agreeing with—but independent of—libration data. Isostatic and tidal stresses are comparable in magnitude. South polar crust is only 7 ± 4 km thick, facilitating the opening of water conduits and enhancing tidal dissipation through stress concentration. Enceladus's resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and shape can be explained in terms of a 99 ± 23 km thick isostatic shell overlying a 65 ± 30 km thick global ocean, thus providing the first clear evidence for a present‐day ocean within Dione.

In a body periodically strained by tides, heating produced by viscous friction is far from homogeneous. I show here that the distribution of the dissipated power within a spherically stratified body is a linear combination of three angular functions. These angular functions depend only on the tidal potential whereas the radial weights are specified by the internal structure of the body. The 3D problem of predicting spatial patterns of dissipation at all radii is thus reduced to the 1D problem of computing weight functions. I compute spatial patterns in various toy models without assuming a specific rheology: a viscoelastic thin shell stratified in conductive and convective layers, an incompressible homogeneous body and a two-layer model of uniform density with a liquid or rigid core. For a body in synchronous rotation undergoing eccentricity tides, dissipation in a mantle surrounding a liquid core is highest at the poles. Within a softer layer (asthenosphere or icy layer), the same tides generate maximum heating in the equatorial region with a significant degree-four structure if the layer is thin. Tidal heating patterns are thus of three main types: mantle dissipation (including the case of a floating icy crust), dissipation in a thin soft layer and dissipation in a thick soft layer. I illustrate the method with applications to Europa, Titan and Io. The formalism described in this paper applies to dissipation within solid layers of planets and satellites for which internal spherical symmetry and viscoelastic linear rheology are good approximations.Comment: 51 pages, 8 figures, accepted for publication in Icaru

22Extreme volcanism on Io results from tidal heating, but its tidal dissipation mechanisms and

Could tidal dissipation within Enceladus' subsurface ocean account for the observed heat flow? Earthlike models of dynamical tides give no definitive answer because they neglect the influence of the crust. I propose here the first model of dissipative tides in a subsurface ocean, by combining the Laplace Tidal Equations with the membrane approach. For the first time, it is possible to compute tidal dissipation rates within the crust, ocean, and mantle in one go. I show that oceanic dissipation is strongly reduced by the crustal constraint, and thus contributes little to Enceladus' present heat budget. Tidal resonances could have played a role in a forming or freezing ocean less than 100 m deep. The model is general: it applies to all icy satellites with a thin crust and a shallow ocean. Scaling rules relate the resonances and dissipation rate of a subsurface ocean to the ones of a surface ocean. If the ocean has low viscosity, the westward obliquity tide does not move the crust. Therefore, crustal dissipation due to dynamical obliquity tides can differ from the static prediction by up to a factor of two.