Laboratoire de Physique de l'Ecole Normale Supérieure

We propose the lattice BGK models, as an alternative to lattice gases or the lattice Boltzmann equation, to obtain an efficient numerical scheme for the simulation of fluid dynamics. With a properly chosen equilibrium distribution, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order of approximation. Compared to lattice gases, the present model is noise-free, has Galileian invariance and a velocity-independent pressure. It involves a relaxation parameter that influences the stability of the new scheme. Numerical simulations are shown to confirm the speed of sound and the shear viscosity.

We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.

International audience

Single linear DNA molecules were bound at multiple sites at one extremity to a treated glass cover slip and at the other to a magnetic bead. The DNA was therefore torsionally constrained. A magnetic field was used to rotate the beads and thus to coil and pull the DNA. The stretching force was determined by analysis of the Brownian fluctuations of the bead. Here the elastic behavior of individual lambda DNA molecules over- and underwound by up to 500 turns was studied. A sharp transition was discovered from a low to a high extension state at a force of approximately 0.45 piconewtons for underwound molecules and at a force of approximately 3 piconewtons for overwound ones. These transitions, probably reflecting the formation of alternative structures in stretched coiled DNA molecules, might be relevant for DNA transcription and replication.

We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.

https://pro.college-de-france.fr/jean.dalibard/publi2/josaB\₈9.pdf

An experimental study of Rayleigh-Bénard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 10 7 < Ra < 6 × 10 12 ) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra . However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu , proportional to $Ra^{\frac{1}{3}}$ while experiment gives an index much closer to $\frac{2}{7}$ . A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.

We report on two experiments using an atomic cascade as a light source, and a triggered detection scheme for the second photon of the cascade. The first experiment shows a strong anticorrelation between the triggered detections on both sides of a beam splitter. This result is in contradiction with any classical wave model of light, but in agreement with a quantum description involving single-photon states. The same source and detection scheme were used in a second experiment, where we have observed interferences with a visibility over 98%.

A central question in developmental biology is whether and how mechanical forces serve as cues for cellular behavior and thereby regulate morphogenesis. We found that morphogenesis at the Arabidopsis shoot apex depends on the microtubule cytoskeleton, which in turn is regulated by mechanical stress. A combination of experiments and modeling shows that a feedback loop encompassing tissue morphology, stress patterns, and microtubule-mediated cellular properties is sufficient to account for the coordinated patterns of microtubule arrays observed in epidermal cells, as well as for patterns of apical morphogenesis.

A microscope employing the characteristics of the reflection at the Brewster angle has been built for the study of first-order phase transitions in monolayers and the growth of two-dimensional domains without adding fluorescent impurities. It takes about 2.4 s to constitute an image.

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow us to calculate the fluctuations and large deviations of the density and the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example, non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.

We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction $U$, are calculated from first principles, using the random-phase approximation. We derive an expression for the frequency-dependent $U(\ensuremath{\omega})$ and show, for the case of nickel, that its high-frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of $U(\ensuremath{\omega})$, so that a model with an energy-independent local interaction can still be used for low-energy properties.

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible due to both significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world-record determinations of critical exponents and correlation function coefficients in the Ising and O(N) models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

Almost half of the total organic carbon (C) in terrestrial ecosystems is stored in forest soils. By altering rates of input or release of C from soils, forest management activities can influence soil C stocks in forests. In this review, we synthesize current evidence regarding the influences of 13 common forest management practices on forest soil C stocks. Afforestation of former croplands generally increases soil C stocks, whereas on former grasslands and peatlands, soil C stocks are unchanged or even reduced following afforestation. The conversion of primary forests to secondary forests generally reduces soil C stocks, particularly if the land is converted to an agricultural land-use prior to reforestation. Harvesting, particularly clear-cut harvesting, generally results in a reduction in soil C stocks, particularly in the forest floor and upper mineral soil. Removal of residues by harvesting whole-trees and stumps negatively affects soil C stocks. Soil disturbance from site preparation decreases soil C stocks, particularly in the organic top soil, however improved growth of tree seedlings may outweigh soil C losses over a rotation. Nitrogen (N) addition has an overall positive effect on soil C stocks across a wide range of forest ecosystems. Likewise, higher stocks and faster accumulation of soil C occur under tree species with N-fixing associates. Stocks and accumulation rates of soil C also differ under different tree species, with coniferous species accumulating more C in the forest floor and broadleaved species tending to store more C in the mineral soil. There is some evidence that increased tree species diversity could positively affect soil C stocks in temperate and subtropical forests, but tree species identity, particularly N-fixing species, seems to have a stronger impact on soil C stocks than tree species diversity. Management of stand density and thinning have small effects on forest soil C stocks. In forests with high populations of ungulate herbivores, reduction in herbivory levels can increase soil C stocks. Removal of plant biomass for fodder and fuel is related to a reduction in the soil C stocks. Fire management practices such as prescribed burning reduce soil C stocks, but less so than wildfires which are more intense. For each practice, we identify existing gaps in knowledge and suggest research to address the gaps.

This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

When a liquid drops impinges a hydrophobic rough surface it can either bounce off the surface (fakir droplets) or be impaled and strongly stuck on it (Wenzel droplets). The analysis of drop impact and quasi static ''loading'' experiments on model microfabricated surfaces allows to clearly identify the forces hindering the impalement transitions. A simple semi-quantitative model is proposed to account for the observed relation between the surface topography and the robustness of fakir non-wetting states. Motivated by potential applications in microfluidics and in the fabrication of self cleaning surfaces, we finally propose some guidelines to design robust superhydrophobic surfaces.

After quantum particles have interacted, they generally remain in an entangled state and are correlated at a distance by quantum-mechanical links that can be used to transmit and process information in nonclassical ways. This implies programmable sequences of operations to generate and analyze the entanglement of complex systems. We have demonstrated such a procedure for two atoms and a single-photon cavity mode, engineering and analyzing a three-particle entangled state by a succession of controlled steps that address the particles individually. This entangling procedure can, in principle, operate on larger numbers of particles, opening new perspectives for fundamental tests of quantum theory.

We have studied the motion of a magnetic domain wall (MDW) driven by a magnetic field H in a 2D ultrathin Pt/Co/Pt film showing perpendicular anisotropy and quenched disorder. MDW velocity measurements down to the so called creep regime show that the average energy barrier scales as $(1/H{)}^{\ensuremath{\mu}}$ with $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.24\ifmmode\pm\else\textpm\fi{}0.04$ and that the correlation function along a MDW is governed by a wandering exponent $\ensuremath{\zeta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.69\ifmmode\pm\else\textpm\fi{}0.07$, in very good agreement with theories giving $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.25$ and $\ensuremath{\zeta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/3$. This is the first direct measurement of the creep regime for a moving interface in a disordered medium.

The limits of validity of the correlation-energy calculations in the regions of high density, low density, and actual metallic electron densities are discussed. Simple physical arguments are given which show that the high-density calculation of Gell-Mann and Brueckner is valid for ${r}_{s}\ensuremath{\lesssim}1$ while the low-density calculation of Wigner is valid for ${r}_{s}\ensuremath{\gtrsim}20$. For actual metallic densities it is shown that the contribution to the correlation energy from long-wavelength momentum transfers ($k<\ensuremath{\beta}{k}_{0}<0.47{{r}_{s}}^{\frac{1}{2}}{k}_{0}$) may be accurately calculated in the random phase approximation. This contribution is calculated using the Bohm-Pines extended Hamiltonian, and is shown to be $E(\ensuremath{\beta})=\left(\ensuremath{-}0.458\frac{{\ensuremath{\beta}}^{2}}{{r}_{s}}+0.866\frac{{\ensuremath{\beta}}^{3}}{{{r}_{s}}^{\frac{3}{2}}}\ensuremath{-}0.98\frac{{\ensuremath{\beta}}^{4}}{{{r}_{s}}^{2}}\right)\left(+0.019\frac{{\ensuremath{\beta}}^{4}}{{r}_{s}}+0.706\frac{{\ensuremath{\beta}}^{5}}{{{r}_{s}}^{\frac{5}{2}}}+\ensuremath{\cdots}\right)\mathrm{ry}.$ An identical result is obtained by a suitable expansion of the result of Gell-Mann and Brueckner; the validity of the Bohm-Pines neglect of subsidiary conditions in the calculation of the ground-state energy is thereby explicitly established. The contribution to the correlation energy from sufficiently high momentum transfers ($k\ensuremath{\gtrsim}{k}_{0}$) will arise only from the interaction between electrons of antiparallel spin, and may be estimated using second-order perturbation theory. The contribution arising from intermediate momentum transfers ($0.47{{r}_{s}}^{\frac{1}{2}}{k}_{0}\ensuremath{\lesssim}k\ensuremath{\lesssim}{k}_{0}$) cannot be calculated analytically; the interpolation procedures for this domain proposed by Pines and Hubbard are shown to be nearly identical, and their accuracy is estimated as \ensuremath{\sim}15%. The result for the over-all correlation energy using the interpolation procedure of Pines is ${E}_{c}\ensuremath{\cong}(\ensuremath{-}0.115+0.031\mathrm{ln}{r}_{s})\mathrm{ry}.$

The fractional quantum Hall states are known to occur in 2-dimensional electron gases. Can they exist in other material systems? Two physicists from France and the U.S. furnish the first unambiguous theoretical proof that they do in fractional Chern insulators.