Table of contents

We provide numerical indications of the q-generalised central limit theorem that has been conjectured (Tsallis C., Milan J. Math., 73 (2005) 145) in nonextensive statistical mechanics. We focus on N binary random variables correlated in a scale-invariant way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called q-product with q ⩽ 1. We show that, in the large-N limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are q_e-Gaussians, i.e., p(x) ∝ [1 − (1 − q_e) β(N)x²]^{1/(1 − q_e)}, with q_e = 2 − [(1)/(q)], and with coefficients β(N) approaching finite values β(∞). The particular case q = q_e = 1 recovers the celebrated de Moivre-Laplace theorem.

Spontaneous nucleation, pulse formation and propagation failure have been observed experimentally in CO oxidation on Pt(110) at intermediate pressures ( ≈ 10 ^{− 2} mbar). This phenomenon can be reproduced with a stochastic model that includes temperature effects. Nucleation occurs randomly due to fluctuations in the reaction processes, whereas the subsequent damping out essentially follows the deterministic path. Conditions for the occurence of stochastic effects in the pattern formation during CO oxidation on Pt are discussed.

We study slow relaxation in dynamics of liquid water at room temperatures and propose a consistent interpretation explaining why liquid-water dynamics exhibits power law relaxation behavior and can form the bottleneck in phase space even though it is a many-dimensional and strongly chaotic system. Our idea is inspired by recent developments of perturbation theories of Hamiltonian systems, and is reminiscent of the so-called Boltzmann-Jeans conjecture. Within this scenario, it is natural to expect that slow relaxation is not limited to liquid-water dynamics. We found that our hypothesis works well in predicting the relaxation properties of other molecules. The relation to the potential landscape picture is also discussed.

We have studied here the influence of the Berry phase generated due to a cyclic evolution of an entangled state of two spin-(1/2) particles. It is shown that the measure of formation of entanglement is related to the cyclic geometric phase of the individual spins.

We report on a measurement of the van der Waals interaction between rubidium atoms in the ground state and a metallic surface, employing a new method involving reflection of laser-cooled atoms from magnetic thin-film atom mirrors. We made use of the fact that the typical distance from which atoms reflect from thin-film magnetic mirrors is of the order of the magnetic domain size and the thickness of the thin film. The modification of the reflectivity of cold atoms from cobalt thin-film magnetic mirrors, with thickness in the range of 200 − 20 nm, due to the competition between the attractive atom-surface interaction and the repulsive magnetic interaction enabled the measurement of the van der Waals force in the range 20–50 nm with an uncertainty of 15%. The measured value agrees well with recent theoretical estimates.

After showing the failure of the traditional heat conduction law in describing correctly the heat flux phenomenon in a rarefied gas at the slip regime, a generalized heat conduction model is presented. The model predicts a heat conduction boundary layer near the wall with a thickness proportional to the Knudsen number. It reduces to the Fourier law when the Knudsen number is sufficiently small. An analytic solution from the present model shows satisfactory agreement with that from gas molecular-dynamics simulation.

The response of turbulent flow to time-modulated forcing is studied by direct numerical simulations of the Navier-Stokes equations. The large-scale forcing is modulated via periodic energy input variations at frequency ω. The response is maximal for frequencies in the range of the inverse of the large eddy turnover time, confirming the mean-field predictions of von der Heydt, Grossmann and Lohse (Phys. Rev. E, 67 (2003) 046308). In accordance with the theory the response maximum shows only a small dependence on the Reynolds number. At sufficiently high frequencies the amplitude of the kinetic energy response decreases as 1/ω. For frequencies beyond the range of maximal response, a significant change in the phase-shift relative to the time-modulated forcing is observed. For large ω the phase shift approaches roughly 90° for the total energy and 180° for the energy dissipation rate.

The effects of flow domain boundaries on the onset of nonlinear flow, and kinetic-energy and energy dissipation densities in three-dimensional heterogeneous porous domains were analyzed. The analyses were based on kinetic-energy and energy dissipation participation numbers, and a 3D lattice Boltzmann model was used to simulate gravity-driven single-phase flow in random porous media. The results revealed that the boundary conditions (periodic vs. no-slip) parallel to the main flow direction have insignificant effects on the magnitude of the critical Reynolds number, that characterizes the onset of nonlinear effects, although it affected the spatial correlations of pore-scale kinetic-energy and energy dissipation densities in all Cartesian directions. Flow domains with periodic boundaries resulted in less-localized (more dispersed) steady-state flows than domains with no-slip boundaries.

Employing computer simulations and Poisson-Boltzmann theory, we show that a symmetric electrolyte in an electric condenser undergoes a localisation-delocalisation transition as a function of the external voltage U. The transition occurs at the critical voltage U_c corresponding to the situation where the surface charge density of the plates equals the area charge density of completely charge-separated electrolytes. The average distance of the electrolyte ions to the plates diverges logarithmically for U↙U_c. This transition is expected to be observable in micro-electrodes.

We study the relaxation modes of an interface between a lyotropic lamellar phase and a gas or a simple liquid. The response is found to be qualitatively different from those of both simple liquids and single-component smectic-A liquid crystals. At low rates it is governed by a non-inertial, diffusive mode whose decay rate increases quadratically with wave number, |ω| = Aq². The coefficient A depends on the restoring forces of surface tension, compressibility and bending, while the dissipation is dominated by the so-called slip mechanism, i.e., relative motion of the two components of the phase parallel to the lamellae. This surface mode has a large penetration depth which, for sterically stabilised phases, is of order (dq²) ^{− 1}, where d is the microscopic lamellar spacing.

The colloidal aggregation problem coupled with sedimentation is stratified, in the sense that the structural and dynamical quantities describing the aggregates depend on the depth at which they are measured. In this work we present the first computer simulation with particles of colloidal aggregation coupled with sedimentation, for which the clusters in the simulation box represent those clusters inside a layer at a fixed depth and of arbitrary thickness in the confinement prism. It would then be possible to compare the results with an eventual validation experiment, in which an aggregating sample is sipped out with a pipette at a fixed depth and subjected to further studies, or with a light scattering experiment in which the laser beam is focused also at a fixed depth in the prism. We confirm the acceleration of the aggregation rate followed by a slowing-down, compared with an aggregating system driven purely by diffusion. We also confirm the appearance of a "sweeping scaling regime" for which the large clusters when drifting downwards sweep smaller ones, which in turn occlude the holes and cavities of these large clusters, increasing in this way their fractal dimension. However, as the large clusters continue to grow for very big depths, and also for medium size clusters at high sedimentation strengths, we have found that the anisotropy of these clusters makes the radius of gyration not to scale with size —becoming impossible to define a fractal dimension— and the clusters become non–self-similar, as found recently by some other authors.

The 300 K structure of soft chemistry synthesized Co_xRh_{1 − x} (x = 0.25, 0.50, 0.75) particles, 1.7 to 2.5 nm large, has been determined by atomic-scale simulations using an interaction model fitted on both ab initio and experimental results. All the measured structural features, strongly different from the ones in the corresponding bulk alloys, have been consistently reproduced. Two major effects, i.e. a strong Co surface segregation and an expansion of the mean bond length, are demonstrated and both are consistent with the drastic enhancement of the magnetization observed in these clusters. Interestingly, the method also provides new insights into interpretation of the experimental results.

A theory for the anomalous vibrational and thermal properties of disordered solids based on the model assumption of randomly fluctuating transverse elastic constants is presented. Mean-field expressions for the vibrational density of states and the energy diffusivity are derived with field-theoretical techniques. As in previous approaches of this type the boson peak (enhancement of the low-frequency density of states) is explained as a result of the frozen-in disorder and compares well with the experimental findings. The plateau in the temperature variation of the thermal conductivity and the behavior beyond the plateau is shown to arise from the enhanced scattering in the boson peak regime and to be essentially a harmonic phenomenon.

We have measured the viscosity of thin polymer films as a function of film thickness using three independent techniques. The results of all methods indicated that the viscosity of the film increases about two orders of magnitude near the solid substrate. Measurements performed on split layer substrates indicated that a layer of polymer chains remained permanently adsorbed at the Si substrate. This layer was responsible for trapping subsequent layers, and propagating the effect of surface interactions to chains without direct contacts to the solid substrate. If this layer was applied prior to the rest of the film, it can screen the surface interactions and even initiate auto-dewetting of other chemically identical layers above it.

The study of the dewetting of very thin polymer films has recently revealed many unexpected features (e.g. unusual rim morphologies and front velocities) which have been the focus of several theoretical models. Surprisingly, one of the most striking features, that is the decrease of the rim width with time, has not yet been explained. In the present letter, we show how the combined effects of a non-linear friction between the film and the substrate, and the presence of residual stresses within the film, result in the presence of a maximum in the time evolution of the rim width. Our model allows a quantitative evaluation of the residual stresses and a characterization of the friction between the polymer film and the substrate. In addition, we show how the introduction of a non-linear friction simply explains the experimentally observed rapid decrease of the dewetting velocity with time.

We investigate electron transfer processes in donor-acceptor systems with a coupling of the electronic degrees of freedom to a common bosonic bath. The model allows to study many-particle effects and the influence of the local Coulomb interaction U between electrons on donor and acceptor sites. Using the non-perturbative numerical renormalization group approach we find distinct differences between the electron transfer characteristics in the single- and two-particle subspaces. We calculate the critical electron-boson coupling α_c as a function of U and show results for density-density correlation functions in the whole parameter space. The possibility of many-particle (bipolaronic) and Coulomb-assisted transfer is discussed.

In order to explain and model the inner ring in photoluminescence (PL) patterns of indirect excitons in GaAs/AlGaAs quantum wells (QWs), we develop a microscopic approach formulated in terms of coupled nonlinear equations for the diffusion, thermalization and optical decay of the particles. The origin of the inner ring is unambiguously identified: it is due to cooling of indirect excitons in their propagation from the excitation spot.

We investigate theoretically the efficiency of the Rashba effect, i.e. the spin-orbit splitting resulting from an electric field. In contrast to previous studies, where the carriers have usually been taken to be electrons, we focus on holes and are able to demonstrate remarkable improvements of the effect by several orders of magnitude. We also show that the frequently-neglected lattice-mismatch between GaAs and AlGaAs can be used to further enhance the efficiency of the wave vector splitting mechanism. The Rashba effect is the fundamental mechanism behind the Datta-Das spin transistor and we find that for a small electric field of 2 kV/cm the spin precession length becomes only 36 nm.

We show that space-charge instabilities (electric-field domains) in semiconductor superlattices are the attribute of absolute negative conductance induced by small constant and large alternating electric fields. We propose an efficient method for the suppression of this destructive phenomenon in order to obtain the generation at microwave and THz frequencies in devices operating at room temperature. We theoretically proved that an unbiased superlattice with a moderate doping subjected to a microwave pump field provides a strong gain at the third, seventh, etc. harmonics of the pump frequency under conditions of suppressed domains.

We study theoretically the spin-polarized Andreev reflection tunneling through a local precessing magnetic spin weakly coupled to a ferromagnet and to a superconductor. The linear Andreev reflection conductance is obtained at zero temperature by using a nonequilibrium Green function approach. It shows that the spin-exchange interaction on the local spin-site can result in two spin-coherent states, from which the Andreev reflection conductance resonance with either a double peak or a single peak is developed. We find that the spin-orbit interaction in the barrier between the local spin-site and the ferromagnet-electrode leads only to a conductance oscillation with base frequency twice the Larmor frequency, 2ω_L, and a variable amplitude with equilibrium chemical potential and spin-flip tunneling coupling.

We have made zero-field current-voltage (IV) measurements of artificially layered high-T_c thin-film bridges. SQUID microscopy of these films provides Pearl lengths Λ longer than the bridge widths, and shows current distributions that are uniform across the bridges. At high temperatures and high currents the voltages follow the power law V ∝ Iⁿ, with n = Φ₀²/8π²ΛkT + 1, in good agreement with the predictions for thermally activated vortex motion. At low temperatures, the IV's are better fit by ln V linear in I ^{− 2}, as expected if the low-temperature dissipation is dominated by quantum tunneling of individual Pearl vortices.

We study the response of the vortex lattice in a strongly type-II 2D superconductor to quasi-static sweeping magnetic induction using the Ginzburg-Landau approach in the lowest Landau level approximation. It is found that, due to small size and relative softness of the vortex core as compared to the atomic core of a typical crystal potential, the vortices tend to flow in independently moving channels with smectic structure. A model for calculating the friction coefficient of moving vortices in the presence of a few pinning centers under conditions of minimal power dissipation is presented.

Superconductivity is a rare example of a quantum system in which the wave function has a macroscopic quantum effect, due to the unique condensate of electron pairs. The amplitude of the wave function is directly related to the pair density, but both amplitude and phase enter the Josephson current: the coherent tunneling of pairs between superconductors. Very sensitive devices exploit the superconducting state, however properties of the condensate on the local scale are largely unknown, for instance, in unconventional high-T_c cuprate, multiple gap, and gapless superconductors. The technique of choice would be Josephson STS, based on Scanning Tunneling Spectroscopy (STS), where the condensate is directly probed by measuring the local Josephson current (JC) between a superconducting tip and sample. However, Josephson STS is an experimental challenge since it requires stable superconducting tips, and tunneling conditions close to atomic contact. We demonstrate how these difficulties can be overcome and present the first spatial mapping of the JC on the nanometer scale. The case of an MgB₂ film, subject to a normal magnetic field, is considered.

In this paper we analyze the effect of a non-trivial topology on the dynamics of the so-called Naming Game, a recently introduced model which addresses the issue of how shared conventions emerge spontaneously in a population of agents. We consider in particular the small-world topology and study the convergence towards the global agreement as a function of the population size N as well as of the parameter p which sets the rate of rewiring leading to the small-world network. As long as p > > 1/N, there exists a crossover time scaling as N/p² which separates an early one-dimensional–like dynamics from a late-stage mean-field–like behavior. At the beginning of the process, the local quasi–one-dimensional topology induces a coarsening dynamics which allows for a minimization of the cognitive effort (memory) required to the agents. In the late stages, on the other hand, the mean-field–like topology leads to a speed-up of the convergence process with respect to the one-dimensional case.