The discovery of superfluidity

Superfluidity is a remarkable manifestation of quantum mechanics at the macroscopic level. This article describes the history of its discovery, which took place at a particularly difficult period of the twentieth century. A special emphasis is given to the role of J.F. Allen, D. Misener, P. Kapitza, F. London, L. Tisza and L.D. Landau. The nature and the importance of their respective contributions are analyzed and compared. Of particular interest is the controversy between Landau on one side, London and Tisza on the other, concerning the relevance of Bose-Einstein condensation to the whole issue, and also on the nature of thermal excitations in superfluid helium 4. In order to aid my understanding of this period, I have collected several testimonies which inform us about the work and attitude of these great scientists.Comment: 30 page

Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps

We investigate limit theorems for Birkhoff sums of locally H\"older functions under the iteration of Gibbs-Markov maps. Aaronson and Denker have given sufficient conditions to have limit theorems in this setting. We show that these conditions are also necessary: there is no exotic limit theorem for Gibbs-Markov maps. Our proofs, valid under very weak regularity assumptions, involve weak perturbation theory and interpolation spaces. For L^2 observables, we also obtain necessary and sufficient conditions to control the speed of convergence in the central limit theorem.Comment: 35 pages v2: minor modifications, clarified titl

Chiral symmetry and spectrum of Euclidean Dirac operator

After recalling some connections between the Spontaneous Breakdown of Chiral Symmetry (SBChS) and the spectrum of the Dirac operator for Euclidean QCD on a torus, we use this tool to reconsider two related issues : the Zweig rule violation in the scalar channel and the dependence of SBChS order parameters on the number N_f of massless flavours. The latter would result into a great variety of SBChS patterns in the (N_f,N_c) plane, which could be studied through so-called Leutwyler-Smilga sum rules in association with lattice computations of the Dirac spectrum.Comment: 6 pages, no figure, class file included. Talk given at the XVII International School of Physics "QCD: Perturbative or Nonperturbative", Lisbon, Portugal, 29 September - 4 October 1999, to appear in the Proceeding

Theory for helical turbulence under fast rotation

Recent numerical simulations have shown the strong impact of helicity on \ADD{homogeneous} rotating hydrodynamic turbulence. The main effect can be summarized through the following law, $n+\tilde n = -4$, where $n$ and $\tilde n$ are respectively the power law indices of the one-dimensional energy and helicity spectra. We investigate this rotating turbulence problem in the small Rossby number limit by using the asymptotic weak turbulence theory derived previously. We show that the empirical law is an exact solution of the helicity equation where the power law indices correspond to perpendicular (to the rotation axis) wave number spectra. It is proposed that when the cascade towards small-scales tends to be dominated by the helicity flux the solution tends to $\tilde n = -2$, whereas it is $\tilde n = -3/2$ when the energy flux dominates. The latter solution is compatible with the so-called maximal helicity state previously observed numerically and derived theoretically in the weak turbulence regime when only the energy equation is used, whereas the former solution is constrained by a locality condition.Comment: 4 page