The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Blocked-micropores,surface functionalized,bio-compatible and silica-coated iron oxide nanocomposites as advanced MRI contrast agent

Quasi-critical fluctuations occur close to critical points or close to continuous phase transitions. In three-dimensional systems, precision tuning is required to access the fluctuation regime. Lowering the dimensionality enhances the parameter space for quasi-critical fluctuations considerably. This enables one to make use of novel properties emerging in fluctuating systems, such as giant susceptibilities, Casimir forces or novel quasi-particle interactions. Examples are discussed ranging from simple metal–adsorbate systems to unconventional superconductivity in iron-based superconductors.     

Air-dispersion measurement by second-harmonic heterodyne interferometry

Interferometers with long optical paths in air usually require knowledge and control of air dispersion. In addition, the measurements at several wavelengths and the dispersion properties of air allow errors caused by air turbulence to be compensated for. An innovative technique for air-dispersion measurement is described for long-baseline ground-based stellar interferometers. The technique combines second-harmonic interferometry and heterodyne detection to permit high-resolution measurement even for low optical powers. Experimental results show measurements of air dispersion in good agreement with the values predicted from the Edlén equation.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.     

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.Preprint Université de Bourgogne-mai 1990     

Brillouin scattering studies of rare gas solids

Abstract

The scattering of light by elementar excitations in the matter is results in two phenomena, discriminated by the zero wavevector frequency of the excitation: if this frequency is zero, one deals with Brillouin scattering, and with Raman scattering in the other case. Brillouin scattering results from the interaction of light with thermal excitations (acoustic phonons in a crystal) of a material, or, from a classical point of view, with density waves. Contrary to Raman scattering, the selection rules allow always the observation of at least one mode. It is a powerful technic in the study of rare gases under pressure: at ambient temperature, rare gases crystallize in the face centered cubic structure (except helium which structure was recently found to be hexagonal) and are therefore Raman and infrared inactive.

Experimental results will be reviewed on rare gases and rare gas mixtures in the fluid phase, like He-Ne and He-H₂. These results will be discussed in relation with recent measurements of the frequency of global oscillations of Jupiter.     

Photoconductivity derived from an exact modelling of the uncompensated one-donor model. III—problem of fitting the exact model with approximate models

Abstract

The paper is essentially devoted to a quantitative comparison of the exact (1D) model developed in Part I, with two approximate models indicated by Kittel (1D_a1) and by Van der Ziel (1D_a2). And this is made for identical values of their common parameters. This allows to show that models 1D and 1D_a1 generally present no suitable intervals for fitting. The model of Van der Ziel is more suited, for, a good fitting with the 1D model can be obtained, for relatively reduced G values, and for temperatures bounded upward by the characteristic temperature T ₀ defined previously. The role played by the sub-models, obtained after simplifying the 1D_ai model equations, is studied also.     

Etude de la structure magnetique et de la transition de typr “spin-flop” de Rb2FeF5

The nature of the magnetic interactions in the chain compound Rb₂FeF₅ has been investigated using neutron diffraction and magnetic measurements under high applied fields. Rb₂FeF₅ orders antiferromagnetically at T_N = 8.0 ± 0.5 K; the magnetic structure is of the A_Z + G_X mode and the moment of the Fe³⁺ ion extrapoled to 0K is 3.5 ± 0.2 μ_B, this low value being due to zero-point spin reduction. Within a chain the Fe³⁺ ions are antiferromagnetically coupled with an exchange constant of J/k = ?8.8 K. A spin-flop behavior has been observed and interpreted on the basis of the molecular field theory. The critical field was found to be H_C = 65 kOe at 1.7 K.