Table of contents

We study recurrent coarse-grained orbits of the nonintegrable stadium billiard and find a singular measure induced by the coarse graining. Recurrent orbits start inside a small disk of radius r with some launching angle α and return to it for the first time after a length L(α). The set S(L) of launching angles α, such that L(α) ⩾ L, is found to have a fractal structure in the limit L → + ∞ with a fractal dimension D such that 1 - D ∼ r/h, function of the Kolmogorov entropy h. This problem is closely related to chaotic scattering where S(L) corresponds to the set of impact parameters giving a "dwell time" larger than L. Numerical results are in agreement with our scaling arguments. Thus, coarse graining allows to connect the dynamical properties of billiards (internal problem) to the (external) problem of chaotic scattering.

A simple model for the coupling of a quantum system to a macroscopic measuring device is proposed, which allows to describe continuous measurements with finite time resolution. It is used to derive a quantum map, generating the dynamics of the quantum kicked rotor under the influence of continuous measurements. Numerical experiments with this quantum map show that the incoherent back-action of the measuring device always destroys dynamical localization on a sufficiently long time scale, and renders the measured dynamics diffusive.

In this letter we study the spectrum of string theory in one dimension starting from the discretized approximation. The sum over all the surfaces with different genus can be formally done for the spectrum and the results can be written in a closed form: a nonperturbative definition of string theory seems possible.

The effect of global density inhomogeneities on spinodal decomposition is studied in two dimensions. We performed lattice gas simulations to show that–except for boundary effects–any spatially varying density profile is conserved during phase separation. This observation is used to interpret spinodal decomposition in a concentration gradient in terms of percolation theory. A relation is established between the coarsening process and the fractal properties of the percolation hull. These results are used to interpret fractal structures observed in experiments of silver deposits in polyimide films.

We evaluate the conversion probability for neutrinos by solving the evolution equations with a numerical method, taking into account a density distribution of the Earth, and calculate an upward-going neutrino flux ratio (ν_e +_e)/(ν_μ +_μ) by using the recent values of atmospheric neutrino fluxes, where the updated ratios ν_μ/_μ and ν_e/_e have been taken into account. It is found that the ratio, including the effect of neutrino-resonant oscillations, can well explain the Kamiokande data for ϕ = 0° and 30°, and the NUSEX and the Fréjus data (averaged over ϕ) at energies around 1 GeV, whilst the ratio with no neutrino oscillations or with the muon polarization cannot explain the measured data.

It is shown by combining the Euler equation of density functional theory with the differential form of the virial theorem that the single-particle kinetic-energy density T_s[ρ], on the minimum, and for N fermions, is a function solely of ρ, ρ' and x. This formal result is illustrated by taking the example of a harmonic oscillator with N levels filled. Model forms of T_s[ρ] and δT_s[ρ]/δρ then follow.

From simple microscopic considerations we propose an expression for the frictional force in granular materials. This force has very nonlinear behavior as a function of the shear rate. The mechanism we propose predicts the existence of a characteristic shear rate, ₀, which separates regions of stable from unstable flow. Our formulation can explain the hysteresis phenomena commonly observed in granular materials.

The solution of a driven nonlinear inhomogeneous Schrödinger equation is investigated. Depending on a control parameter, the definite route from Airy-type stationary solutions to chaotic structures in time is identified as the quasi-periodic Newhouse-Ruelle-Takens route.

The transport of soft-X-ray radiation through thin foil plastic targets, 0.1 and 5 μm thick, has been studied using time-resolved XUV spectroscopy in the 10 to 70 Å spectral wavelength region. An intense source of radiation was produced by overcoating one side of the target with 0.1 μm of gold and irradiating it with green laser light at an intensity between 1·10¹⁴ and 5·10¹⁴ W cm^-2. The experimental results were simulated with a multi-group radiation transport calculation which was coupled to a one-dimensional hydrodynamics model.

The sensitivity of a family of high-gain inertial confinement fusion (ICF) targets to implosion nonuniformities is studied by means of 2-D numerical simulations. The effect of single-wavelength, low-mode number perturbations of the driving pressure is considered. It is shown that the ratio Q of the 2-D target yield to the yield obtained in the spherically symmetric case is a function of the perturbation parameters as well as of the spark convergence ratio and of the 1-D ignition margin of the target. The scaling of Q with mode number and amplitude is derived; it is also shown that tolerable levels of nonuniformities depend critically on the 1-D ignition margin.

The diacetylene bis-p-toluene sulphonate of 2.4-hexadiyne-1.6 diol shows an incommensurate modulated structure between 206 K and 163 K (T_L) in the monomer form. The conversion of about 0.1% monomer into polymer leads to a decrease of T_L by 10 K and to a square-root temperature dependence of the incommensurate component of the modulation wave vector near T_L. This behaviour is ascribed to domain wall wandering caused by the presence of nonsymmetry-breaking random polymer chains, in agreement with theoretical predictions. The unexpected role of these extended frozen defects in the stabilization of a lattice of discommensurations in this type-II incommensurate system is also analysed.

Negative ion mobility in rotating ³He-B at magnetic fields H ≃ 0.1 T has been measured along the common direction of H and the rotation axis Ω. When Ω > 0, we observed an increase of mobility, which originates from a reorientation of the anisotropic energy gap. The increase can be understood quantitatively only if soft vortex cores, predicted by Sonin, are assumed. Their size was found to be on the order of the magnetic Healing length ξ_H.

Using an exact functional renormalization group (RG), we study wetting transitions in d = 1 + 1 dimensions. This RG acts in the function space of the interaction potentials for two interfaces. The RG flow exhibits i) a whole line of fixed points and ii), a separatrix which represents an analytic continuation of the fixed-point line. Numerical and analytical work shows that the line of fixed points almost forms a closed loop in function space. The separatrix, on the other hand, describes a subregime where the wetting transitions are first-order but have unusual scaling properties. A generalization of the RG indicates that these unusual transitions are replaced by usual first-order transitions in d ≠ 1 + 1.

We review the adiabatic (slowly varying confining walls) approximation to the quantized conductance introduced by Glazmann et al. We show that the corrections to this approximation are exponentially small in the smoothness parameter of the constriction. A condition for accurate quantization is given, based on the result that the reflections due to a nonadiabatic widening of the constriction (existing in real devices) would be highly suppressed if a small adiabatic widening and/or a potential barrier should precede the sudden widening. An interesting collimation effect associated with the adiabatic picture is mentioned.

Epitaxially grown YBa₂Cu₃O_x films have been irradiated with 173 MeV ¹²⁹Xe ions. A nonlinear decrease of the critical superconducting transition temperature T_c and an exponential increase of the resistivity ρ is observed. The c-axis parameter is extended to about 12 Å with increasing Xe fluence and the twin boundaries disappear. The 1-2-3 phase is amorphized along the paths of the Xe ions within an area of 40 Å in diameter. A defect-induced enhancement of the critical current density j_c in magnetic fields B is observed after low fluences only if the flux lines are aligned parallel to the amorphized ion traces.

The single-particle Green's function for the strong-coupling limit of the single-band Hubbard model (t-J model) at half-filling is calculated numerically using a Lanczos algorithm. Two-dimensional systems of up to 18 sites with periodic boundary conditions are examined, and evidence is presented for a coherent quasi-particle band of width J which emerges at the low-energy edge of the incoherent spectrum. We find the quasi-particle dispersion to be consistent with ε_k = (J/2)[cos (k_x) + cos (k_y)]², corresponding to effective next-nearest-neighbour hopping.

We study the dynamics of self-assembling rodlike micelles under flow. We assume simple reaction kinetics in which two micelles can fuse only if they are collinear. This provides a positive feedback between micellar alignment and growth, which we study in the regime where micelle-micelle reactions are frequent on the time scale of rotational diffusion. We predict under elongational flow a second-order transition at a critical flow rate, above which a certain fraction of the material forms an aligned "gel" phase of extremely long rods.

Learning from examples to classify inputs according to their Hamming distance from a set of prototypes, in a single-layer network, is studied analytically. Using a statistical mechanical analysis, we calculate the average error, ε, made by the system in classifying novel inputs, as a function of the number of learnt examples. The importance of introducing errors in the learning of the examples is demonstrated. When the number, P, of learnt examples is large, ε decreases as a power law in 1/P, reflecting the absence of a gap in the spectrum of ε.