A short walk through quantum optomechanics

This paper gives a brief review of the basic physics of quantum optomechanics and provides an overview of some of its recent developments and current areas of focus. It first outlines the basic theory of cavity optomechanical cooling and gives a brief status report of the experimental state‐of‐the‐art. It then turns to the deep quantum regime of operation of optomechanical oscillators and covers selected aspects of quantum state preparation, control and characterization, including mechanical squeezing and pulsed optomechanics. This is followed by a discussion of the “bottom‐up” approach that exploits ultracold atomic samples instead of nanoscale systems. It concludes with an outlook that concentrates largely on the functionalization of quantum optomechanical systems and their promise in metrology applications.     

Etude de la restauration de l'aluminium irradié aux electrons (Etape III)

The nature of the electron bombarded aluminium electrical recovery process has been studied by combining quenches with irradiations. Measured Frenkel pair formation rates per incident electrons as well as annealing kinetics emphasize the role of impurity interstitial trapping.     

A diffusion approximation result for two parameter processes

Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle

Summary Given two pointsx, yS ¹ randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth mapf of the circle, we consider for each >0 the point process obtained by recording the timesn>0 such that |f ⁿ (x)–f ⁿ (y)|. With the further assumption that the density of is bounded away from zero, we show that when tends to zero the above point process scaled by –1 converges in law to a marked Poisson point process with constant parameter measure. This parameter measure is given explicity by an average on the rate of expansion off.Partially supported by FAPESP grant number 90/3918-5     

Etude d'impulsions lumineuses breves par interferometrie a deux ondes

We have studied the evolution of the light transmitted through matter in which an optical breakdown is taking place. With a two-waves interferometer made a birefringent plate between polarizers we get informations about the time correlation function of the fields. With an interferometer made of two identical harmonic generating plates separated by a dispersion medium, we learn about the correlation function of the square of the fields. Both systems act as spectral filters with a notch cosine-shaped centered at the incident frequency. We have also observed a transient angular spreading of the beam not previously emphasized which brings a further complication in the picture.     

Kondo lattice and heavy fermions in Heusler phases: CeInAg2−xCux

Magnetic properties, electrical resistivity, specific heat and magnetic excitations have been investigated in Heusler phases CeInAg_2–xCu_x. The hybridization continuously increases from CeInAg₂ (antiferromagnetic Kondo lattice) to CeInCu₂ (heavy fermion compound). The specific heat coefficient for this last compound is found to reach 1.2 J/mole. K² at 1.4 K, the Kondo temperature is 6 K and the Wilson ratio is close to 2.     

On the existence of thermodynamics for the random energy model

Derrida's random energy model is considered. Almost sure andL ^P convergence of the free energy at any inverse temperature are proven. Rigorous upper and lower bounds to the finite size corrections to the free energy are given.     

Moment Systems Derived from Relativistic Kinetic Equations

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie algebras. We then extend this derivation to the classical case and general families of moments that obey the Galilean invariance are also constructed. It is remarkable that the set of formal classical limits of the so-obtained relativistic moment systems is not identical to the set of classical moments quoted in Ref. 21 and one could use a new physically relevant criterion to derive suitable moment systems in the classical case. Finally, the ultra-relativistic limit is considered.