Table of contents

We describe a construction procedure for polycontinuous structures, giving generalisations of bicontinuous morphologies to more than two equivalent, continuous and interwoven sub-volumes. The construction gives helical windings of disjoint graphs on triply periodic hyperbolic surfaces, whose universal cover in the hyperbolic plane consists of packed, parallel trees. The simplest tri-, quadra- and octa-continuous morphologies consist of three (8,3) − c, four (10,3) − a and eight (10,3) − a interwoven networks, respectively. The quadra- and octa-continuous cases are chiral. A novel chiral bicontinuous structure is also derived, closely related to the well-known cubic gyroid mesophase.

For all Einstein-Podolsky-Rosen–type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in non-linear systems the Bell inequality can be violated by non-local effects that are arbitrarily weak. Then we show that the quantum result of the existing Einstein-Podolsky-Rosen–type experiments can be reproduced within deterministic models that include arbitrarily weak non-local effects.

We study the dynamics of N point particles with a gravitational interaction. The divergence of the microcanonical partition function prevents this system from reaching equilibrium. Assuming a random diffusion in phase space we deduce a scaling law involving time, which is numerically checked for 3 interacting masses in a quadratic nonsymmetrical potential. This random walk on the potential energy scale is studied in some detail and the results agree with the numerics.

The notions of pure states and inherent structures, i.e. stable configurations against 1-spin flip are discussed. We explain why these different concepts accidentally coincide in mean-field models with infinite connectivity and present an exactly solvable one-dimensional model where they do not. At zero temperature pure states are to some extent related to k-spin flip stable configurations with k → ∞ after the thermodynamical limit has been taken. This relationship is supported by an explicit analysis of the TAP equations and calculation of the number of pure states and k-spin flips stable configurations in a mean-field model with finite couplings. Finally, we discuss the relevance of the concepts of pure states and inherent structures in finite-dimensional glassy systems.

Taking the Bak-Sneppen evolution model as an example (Phys. Rev. Lett., 71 (1993) 4083), we study extremal dynamics where M > 1 smallest barriers are simultaneously updated as opposed to models in the limit where only the smallest barrier is updated. We investigate the scaling properties of the nearest-neighbour and the random-neighbour model. We demonstrate that the behaviour of models with extremal dynamics in the limit of single update per time step is irrelevant to physical observations.

An irreducible canonical approach to reducible second-class constraints is given. The procedure is illustrated on gauge-fixed two-forms.

The behaviour of a single bubble in blood and in water is studied by using a non-Newtonian model of spherical bubble dynamics. This model considers the compressibility of the liquid surrounding the bubble, the shear-thinning characteristic of liquid viscosity, liquid density and surface tension. It was found that, for values of the maximum bubble radius larger than 10⁻¹ mm, the collapse of a bubble in a constant pressure field in blood is more violent than in water. It suggests that the amount of collateral damage of the biological tissue induced by bubble collapse during high-speed rotational angioplasty and laser-induced angioplasty can be underestimated by experiments in vitro using water as ambient liquid.

A poly(isoprene-b-ethyleneoxide) diblock undergoes multiple ordered state transitions: from a crystalline lamellar (L_c), to a hexagonal (Hex) mesophase, to a bicontinuous cubic phase (Gyroid) before disordering (Dis). We have studied the kinetics of the Hex-to-Gyroid, Hex-to-L_c and L_c-to-Gyroid transitions using synchrotron SAXS and rheology. The Hex-to-Gyroid transformation proceeds via a nucleation and growth mechanism with a small mismatch between the two phases, as anticipated by recent theoretical predictions (M. W. Matsen, Phys. Rev. Lett., 80 (1998) 4470). We provide the first quantitative measure of the activation barrier involved in an order-to-order transition and show the importance of nucleation and growth in these transformations.

The dynamic structure factor, S(Q,E), of liquid lithium (T = 475 K) has been remeasured by inelastic X-ray scattering (IXS) in an extended momentum transfer region (Q = 1.4–110 nm⁻¹) and with improved energy resolution (down to 1.5 meV). These new data on such prototypical simple liquid allow to observe the full evolution with Q from a phonon-like collective mode towards the single-particle dynamics. As a function of Q, one finds: i) at low Q's, a sound mode with a positive dispersion of the sound velocity, ii) at intermediate Q's, excitations whose energy oscillates similarly to phonons in the crystal Brillouin zones, and iii) at high Q's, the S(Q,E) approaches a Gaussian shape, indicating that the single-particle dynamics has been reached.

The dynamics of the ZnCl₄ tetrahedra in the ferroelectric lock-in phase of K₂ZnCl₄ was studied by means of pulsed ³⁵Cl NQR (nuclear quadrupole resonance) techniques. From the temperature dependence of the spin-lattice relaxation rate (1/T_1Q) for each of the triplicated Cl(1) sites in the lock-in phase, it is suggested that the domain peak in the incommensurate phase arises from the ZnCl₄ tetrahedral site with a negligible reorientational motion, whereas the other two sites with an activated reorientational motion lead to the phase solitons.

We report novel results from inelastic neutron scattering measurements at very high momentum transfer, q ⩽ 122 Å⁻¹, performed in supercritical ⁴He, along two very low-density isochores (ρ = 10.35 nm⁻³ and ρ = 13.8 nm⁻³) in the temperature range 5–30 K. The experimental data have been analysed within the framework of the plane-wave Impulse Approximation and the temperature dependence of the single-particle mean kinetic energy has been derived. It is found that this quantity deviates from the classical behaviour in the whole temperature range explored, showing the quantum nature of this system even for these very low-density isochores, the lowest ever experimentally explored. For the higher density, the temperature evolution of the single-particle mean kinetic energy has also been derived using a path-integral Monte Carlo code. These quantum simulation results, as well as those already available for the low-density isochore, are in good agreement with the experimental data. It is pointed out that, at these densities, the temperature dependence of the mean kinetic energy is consistent with an anharmonic behaviour of ⁴He induced by the hard-core component of the interatomic potential.

The ripple topography of ion-beam–eroded surfaces offers a novel method to determine the shape of collision cascades and the distribution of deposited energy. From the energy dependence of the ripple spacing of Ar⁺- and Xe⁺-irradiated graphite surfaces at ion energies between 2 and 50 keV, the relations between mean depth, longitudinal and lateral straggling of the damage cascade were obtained. Their evolution with the ion energy was found to follow power laws for both ion masses and implies an energy-independent lateral spread of the damage cascade, while depth and longitudinal spread scale with the ion energy. This can be explained by the nuclear stopping power being nearly independent of energy in the observed region. High-resolution micrographs of single-ion impacts support this interpretation, as the hillock-shaped surface defects found in the experiments show a lateral extension being independent of the ion energy.

Equations of motion for an anharmonic interface separating two dispersionless 1-d media are shown to be equivalent to those of the Duffing oscillator coupled with an overdamped harmonic oscillator. Transmission and reflection coefficients as well as trapping times are numerically determined for the most representative sets of the model parameters in a large range of frequencies. Abrupt thresholds are found in the transmission and reflection for strong enough anharmonicity. Irregular frequency dependence of the transmission coefficient is found in regions of chaos and almost no frequency dependence in the windows of periodic motion.

We have investigated spreading of superfluid ⁴He on top of polished MgF₂ and evaporated SiO₂ substrates. Our results show strongly varying contact angles of 0–15 mrad on the evaporated layers. According to our theoretical calculations, these contact angles can be explained by a spatially varying distribution of vortex lines, the unpinning velocity of which is inversely proportional to the liquid depth.

The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value U_c of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U = U_c puts a constraint on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.

The nonlinear transport properties of a single-channel quantum wire in the presence of two impurities are investigated. Treating the electron interaction within the Luttinger model, Coulomb oscillations and Coulomb staircase phenomena are identified. Several limiting cases of transport are discussed. The regime of temperatures smaller than the discretization energy of the charge density mode in the dot is treated in detail. For weak to intermediate interaction strengths, the nonlinear current exhibits a peculiar step-like behavior related to the activation of excited plasmonic states. The corresponding differential conductance shows sharp peaks with non-analytic power law line-shape typical of Luttinger liquids.

The ground-state configuration of a system of N electrons or holes (N = 1⋯8) in strongly confined InAs, InP, and Si quantum dots (diameter ∼ 30 Å) is calculated using pseudopotential single-particle energies and wave functions as input to the many-body expansion of the total energy. The validity of generally accepted "rules of level occupation" (Hund's rule, Aufbau principle, and single spin-flip rule) is examined. We find that while Hund's rule is generally obeyed, deviations from the Aufbau principle are common when single-particle energy levels are separated by a few meV. We also find a few instances where the single spin-flip rule is violated, leading to "spin blockade" in linear conductance.

Interference of proximity-induced superconducting correlations in mesoscopic metallic rings is sensitive to the magnetic flux Φ inside these rings. This is the reason for magnetoconductance oscillations in such systems. We detected experimentally and explained theoretically a novel effect: the phase of these oscillations can switch between 0 and π depending on the resistance of intermetallic interfaces and temperature. The effect is due to a nontrivial interplay between the proximity-induced enhancement of the local conductivity and the proximity-induced suppression of the density of states at low energies.

We have measured the differential resistance of mesoscopic gold wires of different lengths connected to an aluminum superconductor as a function of temperature and voltage. Our experimental results differ substantially from theoretical predictions which assume an infinite temperature-independent gap in the superconductor. In addition to taking into account the temperature dependence of the gap, we must also introduce a temperature-dependent inelastic scattering length in order to fit our data.

The random-field Ising model (RFIM) system Fe_0.42Zn_0.58F₂ is studied by magnetization and dynamic susceptibility measurements, under finite dc applied fields (H). For H < 20 kOe, the magnetic behaviour is compatible with a long-range ordered (LRO) antiferromagnetic (AF) ground state, which undergoes a phase transition (PT) at a critical temperature T_c(H). For higher H, the LRO configuration becomes unstable and the PT is destroyed. A glassy dynamics emerges in the upper part of the (H,T) phase diagram. Our results reconcile earlier concepts associated with the weak RFIM problem with recent experimental data in Fe_xZn_{1 − x}F₂.

The tunnel magnetoresistance and its connection to the interlayer exchange interaction is studied in ferromagnet-insulator-ferromagnet junctions. Building on the non-equilibrium Keldysh formalism, we include a contact interaction between localized spins and conduction electrons and derive an expression for the tunnel current that depends on the magnetization of the layers as ⟨S_L·S_R⟩ in correspondence with the exchange coupling. From this expression we also obtain a formula for the tunnel magnetoresistance. At low bias and for systems where one can neglect size-quantization effects Julliere's formula is rederived. The temperature dependence of the dynamical parameters arises from the system of localized spins, its interaction with the conduction electrons, and the thermal reservoirs.

The propagator of the Fokker-Planck equation with a linear force is determined using Green's function technique on the space of generalized functions. It is shown that our result is identical with that obtained by Lo within the framework of Lie algebraic approach.

We point out that one of a pair of isospectral shapes subjected to a certain intentionally altered building scheme would be expected to lose isospectrality because of the mathematical form of a relevant spectral function expansion which involves angles. A higher "calibration" mode which has common exactly specified eigenfrequency for all three shapes is mentioned.