Table of contents

The paper discusses the problem of correspondence between the classical and quantum approaches to the description of chaotic dynamics of a mesoscopic particle. The condition for the equivalence of both approaches is given.

The relationship between the geometrical structure of weight space and replica symmetry breaking (RSB) in multilayer neural networks is studied using a toy model. The distribution of sizes of the disconnected domains of solution space is computed analytically and compared to the RSB calculation of the Gardner volume. We are able to show explicity that ergodicity breaking and RSB are not equivalent. Repeating these calculations using the cavity approach allows us to interpret the geometrical meaning of a RSB ansatzd.

We consider the surface critical behaviour of a semi-infinite two-dimensional layered Ising model, where the couplings perpendicular to the surface follow the aperiodic Rudin-Shapiro sequence. The model has unusual critical properties: depending on the strength of the modulation, at the bulk critical point the surface magnetization is either discontinuous or vanishes with an essential singularity. The critical surface magnetization as well as the form of the essential singularity are calculated exactly.

The specific mechanism of self-organization to a critical state is identified for the Bak-Sneppen evolution model. This model is mapped exactly to an underlying branching process. Theoretical arguments, supported by numerical simulations, indicate that the resulting critical behavior is in the same universality class as Reggeon field theory.

A method to distinguish low-dimensional chaos from randomness is presented. Autoregressive processes are fitted to the data and forecasts are obtained on the basis of the model selected. Two possible forecasting techniques are distinguished. The global autoregressive approximation views the data as a realization of a linear stochastic process, whereas the local autoregressive approximation views the observations as the realizations of a chaotic process. The comparison between the predictive skills of the two techniques allows us to gain insight into distinguishing chaos from randomness.

We have theoretically studied a one-dimensional light field configuration which combines velocity-selective coherent-population trapping with the action of a novel kind of sub-Doppler force providing efficient cooling below the recoil limit. The force is based on velocity-induced non-adiabatic passage of atomic population from the non-coupling state to the light-shifted coupling state. We show for ⁸⁷Rb that within 0.88 ms 35% of an initial distribution of 12ℏk width can be cooled into a 0.5ℏk momentum interval, and that more than 90% of the initial distribution are still confined to 12ℏk width.

The position of a polarized atom passing through a standing light wave can be localized by observing the phase of the atomic-dipole moment in a Ramsey-type experiment. Depending on the outcome of the measurement, the diffraction pattern in the far field corresponds to atoms with their momentum changed by integer multiples of 4ℏk. Position measurements with standard deviation of ≈ λ/40 seem to be possible with optical techniques.

We propose a scheme for observing the inhibition of quantum tunneling of an atom trapped in a double-well potential due to continuous observation of light scattering. A resonant laser beam is focused in one of the wells. Continuous measurement of the position of the atom is performed by observing the presence (or absence) of photons emitted by the atom. An interpretation in terms of a quantum Zeno effect is given.

Numerical and experimental results indicate that the critical amplitude for non-linear growth of disturbances in a uniform shear flow follows two scaling laws, depending on the shape of the initial disturbance: i) a Re^-1 law for disturbances with zero streamwise dependence (streaks) (Kreiss et al., submitted to J. Fluid Mech.); ii) a Re^-0.4±0.1 law for disturbances with non-zero streamwise dependence (spots) (Dauchot and Daviaud, submitted to Phys. Fluid A). It is shown that these laws can be explained by the competition between non-linear growth and viscous dissipation and that the difference in exponent simply reflects the difference in viscous-decay mechanism. Lower bounds for conditions for non-linear growth are derived analytically. They follow a Re^-1 and Re^-1/3 law for streamwise and spotwise initial perturbations. The transition to a self-sustained turbulent state is also discussed. Upper bounds for this transition are derived. They follow, respectively, a Re^-1/2 and Re^-1/6 law for streak or spot initial perturbations.

The cylindrical kinetic Fokker-Planck equation used in plasma physics is integrated in the short-transition-time approximation. The transition probability obtained is adjusted for its use in numerical computations so that both density and energy are conserved for any number of time iterations.

The growth of micron-size carbon fibres from thermal decomposition of hydrocarbons catalyzed by a metal has been widely studied. Coil-shaped fibres often grow among straight or twisted filaments. Their internal structure has not been studied in detail as yet. In the present work, the thermal cracking of acetylene on Co nanoparticles dispersed on porous silica has produced relatively well graphitized hollow nanotubules, including straight filaments and regular helices. The small diameter of the coiled tubules and the absence of an amorphous coating allowed a determination of their texture by transmission electron microscopy (TEM). The coiled tubules consist of regularly polygonized, coaxial graphene tubes whose angular bends are aligned. The bends are probably caused by the occurrence along the helix of pairs of pentagon-heptagon carbon rings in the hexagonal network. Such a structure was recently predicted to be a thermodynamically stable topology for helical, single-sheet carbon tubes. A molecular model, consistent with theoretical predictions on how to connect cylindrical tubule segments, is provided.

We report ab initio calculations of the electronic structure of large-unit-cell approximant phases to icosahedral Ti-transition-metal quasi-crystals and of disordered alloys of the same composition. Our results demonstrate that the approximant phase is stabilized relative to the body-centred solid solution by the formation of a broad pseudogap at the Fermi level. The conditions for the formation of the pseudogap are discussed in relation to the atomic structure.

A two-dimensional (2D) system of classical dipoles free to rotate in a plane and fixed on an N × N square lattice (N ⩽ 32) has been studied as a function of temperature (for thermal energies less than the typical magnetic energy). Spin dynamics simulations have been performed using periodic boundary conditions and the spin-wave excitation spectra measured. A long-lived mode related to a continuous degeneracy of the ground state of this system has been observed. A calculation to study both librational and rotational motion in this mode has been made. In the librational regime the measured frequencies are in good quantitative agreement with the calculations. For systems below a critical size the rotational regime of this mode is observed. The critical size predicted by the theory is in fair agreement with the observations.

The relaxation time of the magnetization of a big magnetic molecule is evaluated. Isotropic exchange is assumed to be dominant, resulting in a fixed spin modulus s (equal to 20 in the case of interest). A perturbation of the form AS_z² results from spin-orbit coupling and produces an energy barrier As² which separates positive and negative values of S_z. Spin-phonon interactions are treated by second-order perturbation theory. An upper limit of the pre-exponential factor in the Arrhenius law is obtained, which is consistent with the very large experimental value.

Hubbard tight-binding Hamiltonian is used to derive the local magnetic moments of low-index and vicinal V surfaces. The polarization of the low-index surface atoms can be qualitatively explained through the coordination number rule but inwards relaxation tends to suppress it. For vicinal surfaces, both the single-cell and double-cell magnetic periodicities are considered. The magnetic moments at the edge of the step are much lower than on their neighbouring atoms in the plane of the step and to atoms of the less coordinated crystallographic faces (100) and (111).