Personal reflections on the history of aperiodic crystals from early days to the state of the art

International audienceAperiodic crystals occur as modulated, intergrowth and quasicrystal structures. Their characterization in terms of symmetries possibly requires not only a higher-dimensional description, but also non-Euclidean transformations (like scaling). These crystallographic symmetries, observed in nature, have been investigated but only partially classified. Turning points in the structure determination of aperiodic crystals are presented in historical perspective up to the present time, together with methods and programs. The WEB allows to get more information on all that, on additional tools and on databases. An attempt to present challanges towards lines of future research concludes the review

Error-Free 10.7 Gb/s Digital Transmission over 2 km Optical Link Using an Ultra-Low-Voltage Electro-Optic Modulator

We demonstrate the feasibility of 10.7 Gb/s error-free (BER < 10-12) optical transmission on distances up to 2 km using a recently developed ultra-low-voltage commercial Electro-Optic Modulator (EOM) that is driven by 0.6 Vpp and with an optical input power of 1 mW. Given this low voltage operation, the modulator could be driven directly from the detectors’ board signals without the need of any further amplification reducing significantly the power dissipation and the material budget

Estudo da curva de crescimento de bubalinos da raça Murrah criados no estado do Rio Grande do Sul.

Objetivou-se identificar um modelo, dentre oito citados na literatura, que melhor descreva a curva de crescimento de bubalinos da raça Murrah criados no estado de Rio Grande do Sul. Foram utilizadas informações de 42 machos e 48 fêmeas da raça Murrah, nascidos entre 2009 e 2011, totalizando 624 pares de registros peso-idade do nascimento até 750 dias de idades. Os parâmetros dos modelos foram estimados por meio de regressão não-linear pelo procedimento NLIN (SAS system), utilizando-se o método de Gauss Newton. Os critérios para a escolha do melhor ajuste foram: o quadrado médio dos resíduos (QMR), o desvio médio absoluto (DMA), o índice e a avaliação visual do gráfico dos valores observados e estimados. Com base no do QMR, DMA e o índice, constatou-se que o modelo Richards (1959) apresentou melhor ajuste, seguido pelo modelo Von Bertalanffy (1957). Com isto, o modelo Richards (1959) dentre os testados foi capaz de descrever o crescimento de búfalos da raça Murrah criados no estado do Rio Grande do Sul

Theory of Superconducting TcT_{c} of doped fullerenes

We develop the nonadiabatic polaron theory of superconductivity of $M_{x}C_{60}$ taking into account the polaron band narrowing and realistic electron-phonon and Coulomb interactions. We argue that the crossover from the BCS weak-coupling superconductivity to the strong-coupling polaronic and bipolaronic superconductivity occurs at the BCS coupling constant $\lambda\sim 1$ independent of the adiabatic ratio, and there is nothing ``beyond'' Migdal's theorem except small polarons for any realistic electron-phonon interaction. By the use of the polaronic-type function and the ``exact'' diagonalization in the truncated Hilbert space of vibrons (``phonons'') we calculate the ground state energy and the electron spectral density of the $C_{60}^{-}$ molecule. This allows us to describe the photoemission spectrum of $C_{60}^{-}$ in a wide energy region and determine the electron-phonon interaction. The strongest coupling is found with the high-frequency pinch $A_{g2}$ mode and with the Frenkel exciton. We clarify the crucial role of high-frequency bosonic excitations in doped fullerenes which reduce the bare bandwidth and the Coulomb repulsion allowing the intermediate and low-frequency phonons to couple two small polarons in a Cooper pair. The Eliashberg-type equations are solved for low-frequency phonons. The value of the superconducting $T_{c}$, its pressure dependence and the isotope effect are found to be in a remarkable agreement with the available experimental data.Comment: 20 pages, Latex, 4 figures available upon reques

Relativistic nature of a magnetoelectric modulus of Cr_2O_3-crystals: a new 4-dimensional pseudoscalar and its measurement

Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we extract a 4-dimensional relativistic invariant pseudoscalar $\widetilde{\alpha}$. It is temperature dependent and of the order of 10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, $\widetilde{\alpha}$ is for Cr_2O_3 what Tellegen's gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.Comment: Revtex, 36 pages, 9 figures (submitted in low resolution, better quality figures are available from the authors

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Experimental investigation of 4-dimensional superspace crystals

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