Table of contents

The quantum corrections make the event horizon of a black hole capable of reflection: any particle that approaches the horizon can bounce back in the outside world. The albedo of the horizon depends on the black-hole temperature. The reflection shares physical origins with the phenomenon of Hawking radiation; both effects are explained as consequences of the singular nature that the event horizon exhibits on the quantum level.

The phenomenon of spatial coherence resonance is presented and studied. Specifically, we show that spatiotemporal noise is able to optimally extract an intrinsic spatial scale in nonlinear media close to (but before) a pattern-forming instability. This effect is observed in a model of pattern-forming chemical reaction and in the Swift-Hohenberg model of fluid convection. In the latter case, the phenomenon is described analytically via an approximate approach.

Coupled map networks evolve from sparsely connected random graphs to small-world networks according to a simple adaptive rewiring algorithm. This evolution is known to occur for networks of a constant number of units and connections, and system parameters, including uniform connection strength, if the maps are chaotic. The present study investigates the consistency of the generated structures. Evolution to small-world networks is shown to occur over a wide range of network sizes above a certain threshold. The distribution of the connections reveals hierarchical structures for larger networks. In spite of high variability in the number of connections of each unit, for a given network size the number of clusters evolving shows a remarkable uniformity.

We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so that the ensemble is inhomogeneous with respect to the internal variable. Interactions between oscillators depend on this variable and thus vary with time. We show that, as the inhomogeneity of time scales in the internal evolution grows, the system undergoes a critical transition between ordered and incoherent states. This transition is mediated by a regime of dynamical clustering, where the ensemble recurrently splits into groups formed by varying subpopulations.

The fractal behaviour of medium-energy knocked-out protons in angular and azimuthal phase space for ²⁸Si-AgBr interactions at 14.5 A GeV has been studied using Takagi's method. The generalized dimensions (D_q) are determined from this method. The data reflects the monofractal behaviour of medium-energy knocked-out protons.

We investigate the electronic structure and properties of Rydberg atoms exposed to a magnetic quadrupole field. It is shown that the spatial as well as generalized time-reversal symmetries lead to a two-fold degeneracy of the electronic states in the presence of the external field. A delicate interplay between the Coulomb and magnetic interactions in the inhomogeneous field leads to an unusual weak field splitting of the energy levels as well as complex spatial patterns of the corresponding spin polarization density of individual Rydberg states. Remarkably, the magnetic quadrupole field induces a permanent electric-dipole moment of the atom.

We directly measure the cross-phase shift and nonlinear refractive index of a three-level Λ-type hot atomic coherence system inside an optical ring cavity. The cross-phase nonlinear index of refraction n₂ is significantly enhanced and sharply changed when the conditions of atomic two-photon resonance are closed. The cross-phase shift of π induced by controlling light on the probe wave has been observed under a relatively low controlling power of 16.2 mW. The system is valuable in developing optical devices for the optical information process.

The ingenious idea of single-molecule imaging by hard X-ray Free Electron Laser (X-FEL) pulses was recently proposed by Neutze et al. (Nature406 (2000) 752). However, in their numerical modelling of the Coulomb explosion, several interactions were neglected and no reconstruction of the atomic structure was given. In this work we carried out improved molecular-dynamics calculations including all quantum processes which affect the explosion. Based on this time evolution, we generated composite elastic-scattering patterns, and by using Fienup's algorithm successfully reconstructed the original atomic structure. The critical evaluation of these results gives guidelines and sets important conditions for future experiments aiming at single-molecule structure solution.

We consider a toy model for glassy dynamics of colloidal suspensions: a single Brownian particle diffusing among immobile obstacles. If Gaussian factorization of static density fluctuations is assumed, this model can be solved without factorization approximation for any dynamic correlation function. The solution differs from that obtained from the ideal mode coupling theory (MCT). The latter is equivalent to including only some positive-definite terms in an expression for the memory function. An approximate re-summation of the complete expression suggests that, under the assumption of Gaussian factorization of static fluctuations, mobile particle's motion is always diffusive. In contrast, MCT predicts that the mobile particle becomes localized at a high enough obstacle density. We discuss the implications of these results for models for glassy dynamics.

We analyse the universal properties of nonequilibrium steady states of driven magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the symmetries of the two-point correlation functions. We, for the first time, also suggest the intriguing possibility of multiscaling universality class varying continuously with certain dimensionless parameters. The experimental and theoretical implications of our results are discussed.

We demonstrate the existence of a form of topological order in the Luttinger liquid state, which appears crucial to the notion of spin-charge separation. This order, which is closely related to the hidden order characterizing the Haldane spin chains, appears to be incompletely specified in the Tomonaga-Luttinger picture from bosonization. Thus, we use numerical calculations to complete the picture.

The first-principles SIC-LSD theory is utilized to study electronic, magnetic and orbital phenomena in LaMnO₃. The correct ground state is found, which is antiferro orbitally ordered with the spin magnetic moments antiferromagnetically aligned. Jahn-Teller energies are found to be the largest energy scale. In addition, it is the Jahn-Teller interaction which is the dominant effect in realizing orbital order, and the electronic effects alone do not suffice.

We demonstrate movement of a head-to-head domain wall through a magnetic nanowire of permalloy (Ni₈₁Fe₁₉) simply by passing an electrical current through the domain wall and without any external magnetic field applied. The effect depends on the sense and magnitude of the electrical current and allows direct propagation of domain walls through complex nanowire shapes, contrary to the case of magnetic-field–induced propagation. The efficiency of this mechanism has been evaluated and the effective force acting on the wall has been found equal to 0.44 × 10⁻⁹ N A⁻¹.

The phase diagram of vortex states in the plane of density of columnar defects vs. temperature is obtained by large-scale Monte Carlo simulations of the three-dimensional anisotropic, frustrated XY model. At low temperatures and low densities of columnar defects, a phase characterized by hexagonal Bragg peaks and the diverging tilt modulus is observed, which may be the Bragg-Bose glass phase. As the temperature increases, the first-order melting transition to the interstitial liquid takes place. This melting temperature increases along with the density of columnar defects owing to "selected pinning" of flux lines. When the density of defects further increases, the transition to the Bose glass phase occurs.

We have investigated the dissipative behaviour of MgB₂ textured thin films at different perpendicular magnetic fields H and bias currents J, to study activation energy dependencies U(J) and U(H). For J < J*, where J* is a magnetic-field–dependent crossover current, activation energies are weakly current dependent, U(J) ≈ const, while, for J > J*, U(J) ∼ – ln J. At J < J*, the magnetic-energy dependencies are logarithmic, U(H) ∼ – ln H, while for J > J*, U(H) ∼ H^–1, up to μ₀H ≈ 5 T. The J*(H) curve separates two zones with different vortex dynamics. We discuss the J*(H) curve in terms of a current-driven transition from a thermally activated flux flow to a flux creep regime. For pronounced disorder, the data suggest the influence of the activation energy distribution on the U(J) and U(H) dependencies.

We have investigated the nucleation of superconductivity in an Al mesoscopic disk, with a magnetic dot on the top. The dot is magnetized perpendicularly, and its magnetic field is inhomogeneous. The Al disk and magnetic dot are separated by an insulating layer, which ensures that there is only magnetic interaction between them. This hybrid superconductor/ferromagnet structure exhibits the maximum critical temperature for a finite value of the perpendicular applied magnetic field, which is parallel to the magnetization of magnetic dot. We have found a good agreement between the experimental data for the superconductor/normal metal phase boundary and the theoretical predictions based on the Ginzburg-Landau theory.

Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted molecular-beam epitaxy. Correlated SIMS, structural and magnetic measurements show that the incorporation of Mn strongly depends on the conditions of the growth. Hysteresis loops which persist at high temperature do not appear to be correlated to the presence of Mn. Samples with up to 2% Mn are purely substitutional Ga_{1 − x}Mn_xN epilayers, and exhibit paramagnetic properties. At higher Mn contents, precipitates are formed which are identified as GaMn₃N clusters by X-ray diffraction and absorption: this induces a decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg exhibit a new feature: a ferromagnetic component is observed up to T_c ∼ 175 K, which cannot be related to superparamagnetism of unresolved magnetic precipitates.

Proximity effects in an [Er₂₀|Tb₅] superlattice lead to the formation of new magnetic phases. Modulated magnetic order, expected for pure Er, and ferromagnetic order, expected for pure Tb, coexist at low temperatures. Employing X-ray resonance exchange scattering, we could probe directly the respective spin polarisations of the conduction band electrons, providing a mechanism for the interlayer coupling. The different anisotropies of Er and Tb compete with this tendency to long-range magnetic order, leading to substantial thermal-hysteresis effects.

We study the role of liquid films for light transport in dry foams based on ray optics. The foams are modelled by two-dimensional Voronoi tessellations with varying degree of disorder. We perform extensive simulations to determine the diffusive limit of light for two models. In model I, we choose a constant intensity reflectance r to explore the effect of disorder. We show that the honeycomb structure sets the right order of magnitude for the diffusion constant D by providing a master curve for D(r), whereas disorder reveals itself in a fine structure. In model II, the reflectance for thin films as determined by Fresnel's formulae is chosen as well as some disorder in the film thickness. We argue that this model reproduces experimental features and the right order of magnitude for the diffusion constant. This suggests that the liquids films in combination with ray optics are relevant for explaining photon diffusion in foams.

We develop a propagating-front analysis, in terms of a local probability of zipping, for the helicase activity of opening up a double-stranded DNA (dsDNA). In a fixed-distance ensemble (conjugate to the fixed-force ensemble), the front separates the zipped and unzipped phases of a dsDNA and a drive acts locally around the front. Bounds from variational analysis and numerical estimates for the speed of a helicase are obtained. Different types of helicase behaviours can be distinguished by the nature of the drive.

The district of Southern California and Japan are divided into small cubic cells, each of which is regarded as a vertex of a graph if earthquakes occur therein. Two successive earthquakes define an edge or a loop, which may replace the complex fault-fault interaction. In this way, the seismic data are mapped to a random graph. It is discovered that an evolving random graph associated with earthquakes behaves as a scale-free network of the Barabási-Albert type. The distributions of connectivities in the graphs thus constructed are found to decay as a power law, showing a novel feature of earthquake as a complex critical phenomenon. This result can be interpreted in view of the facts that the frequency of earthquakes with large values of moment also decays as a power law (the Gutenberg-Richter law) and aftershocks associated with a mainshock tend to return to the locus of the mainshock, contributing to the large degree of connectivity of the vertex of the mainshock. Thus, a mainshock plays the role of a "hub". It is also found that the exponent of the distribution of connectivities is characteristic for the plate under investigation.