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[en] This paper presents recent progress on the calculation of the critical temperature of a superconductor from Eliashberg theory. First the authors solve exactly the Eliashberg equations for the critical temperature in the weak coupling limit λ, μ* → 0 for a general Eliashberg function α²Fμ. This provides informations complementary of those already obtained from the strong coupling side. The authors obtain results somewhat analogous to what is known in the strong coupling regime. The authors show that in the weak coupling regime the best choice for characteristic frequency is ω_log in the sense that the dependence of T_c on the shape of α²F(ω) is optimally included in this way. However there is an additional dependence of T_c on the spectral shape of α²F(ω). Moreover the authors obtain that, in this weak coupling regime, the critical temperature depends only on the large scale structure of the spectrum. The authors use this knowledge to propose an interpolation formula which bridges between the weak and the strong coupling regimes. Its qualitative and quantitative behavior is in very good agreement with numerical results

[en] The sound attenuation due to collisions in superfluid ³He is studied, using for the collision integral a simplifying ansatz which satisfies conservation laws. In the zero-sound regime, attenuation and velocity are fairly frequency independent; this supports the idea that collisions can be accounted by a mere background in sound attenuation. In the first-sound regime, the viscosity tensor is studied (in the A phase) and its low-temperature behavior investigated

[en] The general expression for the energy functional relevant for non-linear hydrodynamics of superfluid ³He is investigated. A number of new terms which had not been considered before are found. There is little change in the formal equations of hydrodynamics but the explicit content is significantly modified. (author)

[en] Orbital waves in the A phase of superfluid ³He are shown to be essentially diffusive. The weak-coupling expression for the ''angular superfluid density'' tensor C is obtained

[en] High-tc superconductivity was discovered in 1986. The prospects of being able to dispose of superconductors cooled by liquid nitrogen instead of liquid helium, and fundamental physics questions raised by these new compounds drag an unprecedented scientific mobilization. Today, the super conductive state nature become clearer. But, to all expectations, their normal state nature is proved to present quite more difficulties. 20 refs., 5 figs

[en] We show that there is no ground to the doubts raised by Ho and Mermin about the validity of the recently proposed modifications of ³He hydrodynamics. Contrary to what they claim, the modified equations do have rotating equilibrium as a solution

[en] The authors study in general terms the ratio 2Δ/T_c within Eliashberg theory of super-conductivity. They point out that, in the calculation of 2Δ/T_c it is possible to replace in a systematic and explicit way any boson spectrum by a two Einstein peak spectrum, without changing the result by more than a few percent. This allows to reduce the general problem to a 4 parameters problem and makes it possible to extract from 2Δ/T_c the maximum information on the boson spectrum. They make use of this two peak representation to obtain a complete description of all the possible outcome for the value of 2Δ/T_c. The authors find specific correlations between some characteristic averages of the boson spectrum and the value of 2Δ/T_c, which are far from perfect but are good enough for practical use. As an example they apply these results to the specific cases of the cuprates and the fullerenes superconductors in order to show how the knowledge of 2Δ/T_c can help to narrow the possible origins of the pairing mechanism. Finally they give interpolation formulae which allow to bypass the numerical calculation of 2Δ/T_c from Eliashberg equations and still provide the answer with a precision which is quite enough for practical purposes

[en] Orbital dynamics for zero wavevector q=0 is studied at low temperature. The consequences for low temperature NMR are investigated. (Auth.)

[en] A microscopic theory for orbital dynamics obtained from kinetic theory is presented. Only homogeneous systems are considered. The main interest of the theory is to provide microscopic treatment for the hydrodynamic regime and the collision regime. The treatment is parallel to a preceding theory of spin dynamics. The motion of the order parameter is eliminated in the matrix kinetic equation by canonical transformation. Then after diagonalization, a scalar kinetic equation for Bogoliubov quasiparticles is obtained. The set of equation is completed by a conservation law. Because of the invariance of the system under rotation of the orbital variables, the canonical transformation is k-space rotation, and the related conservation law is the angular momentum conservation law. (Aoki, K