Table of contents

We study the critical Casimir force in a d-dimensional L_∥^d-1×L slab geometry with a finite aspect ratio ρ=L/L_∥ above, at, and below T_c on the basis of the O(n) symmetric isotropic φ⁴ field theory with short-range interactions. Exact results are obtained in the large-n limit. For n=1, the result of a perturbation approach at fixed dimension d=3 is presented that describes the dependence on the aspect ratio in the range ρ≳1/4. Our analytic result for the Casimir force scaling function for ρ=1/4 agrees well with recent Monte Carlo data for the three-dimensional Ising model in slab geometry with periodic boundary conditions above, at, and below T_c.

Out-of-equilibrium magnetised solutions of the XY-Hamiltonian Mean-Field (XY-HMF) model are built using an ensemble of integrable uncoupled pendula. Using these solutions, we display an out-of-equilibrium phase transition using a specific reduced set of the magnetised solutions.

It is shown that the formula of the isometry generators of the spinor representation given by Carter and McLenaghan is universal in the sense that this holds for any representation, in either local frames or even natural ones. Starting with the observation that point-dependent spin matrices in natural frames can be defined for any tensor representation, the covariant form of the isometry generators is written down, showing that this is just the Carter and McLenaghan formula in natural frames.

It is shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the universe. This is due to the presence of a third mode of polarization in the linearized gravity in which a "curvature" energy term is present. Such an energy can, in principle, be identified as the Dark Energy. The model can also help to a better understanding of the framework of the Einstein-Vlasov system.

The study of the entanglement properties of systems of N fermions has attracted considerable interest during the last few years. Various separability criteria for pure states of N identical fermions have been recently discussed but, except for the case of two-fermions systems, these criteria are difficult to implement and are of limited value from the practical point of view. Here we advance simple necessary and sufficient separability criteria for pure states of N identical fermions. We found that to be identified as separable, a state has to comply with one single identity involving either the purity or the von Neumann entropy of the single-particle reduced density matrix. These criteria, based on the verification of only one identity, are drastically simpler than the criteria discussed in the recent literature. We also derive two inequalities verified, respectively, by the purity and the entropy of the single-particle, reduced density matrix, which lead to natural entanglement measures for N-fermion pure states. Our present considerations are related to some classical results from the Hartree-Fock theory, which are here discussed from a different point of view in order to clarify some important points concerning the separability of fermionic pure states.

It is shown that scalar particles can tunnel across the event horizon in charged Reissner-Nordström and Reissner-Nordström-de Sitter black holes to yield the correct Bekenstein-Hawking entropy.

We describe the dynamics of a bound state of an attractive δ-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the initially confined wave function remains confined to the moving potential. However, it is shown that besides the probability to remain confined to the moving barrier and the probability to remain in the initial position, there is also a certain probability for the particle to move at double speed. A quasi-classical interpretation for this effect is suggested. The temporal and spectral dynamics of each one of the scenarios is investigated.

We discuss the temporal evolution of correlations of synchronization errors in spatially extended chaotic systems near (and below) the synchronization transition. We exploit the fact that, by construction, synchronization errors are finite perturbations of the coupled system in order to analyze the dynamics of the error and how their properties are determined by the nearby phase transition. We introduce a novel diagram plot that allows us to identify the transition universality class in a very intuitive and computationally inexpensive way.

The extended semantic realism (ESR) model proposes a new theoretical perspective that embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables introduced by the ESR model. By using this representation, we supply a straightforward generalization of the projection postulate and justify it in the case of discrete generalized observables by introducing a reasonable physical assumption on the evolution of the compound system made up of the (microscopic) measured system and the (macroscopic) measuring apparatus.

Boltzmann's principle is used to select the "most probable" realisation (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles (N≪∞), for both classical and quantum statistics. The inferred probability distributions provide the means to define intensive variables and construct thermodynamic relationships for small microcanonical systems, which do not satisfy the thermodynamic limit. This is of critical importance to nanoscience and quantum technology.

Using the results from Schramm Löwner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various two-dimensional domain geometries. We generalize to two polymers and examine whether the fluctuation force can trap the object into a stable equilibrium. We compute the force exerted on the objects at the domain boundary, and the force mediated by the polymer between such objects. The results can straightforwardly be extended to any SLE interface, including Ising, percolation, and loop-erased random walks. Some are relevant for extremal value statistics.

Electron transmission through insulating Al₂O₃ nanocapillaries of different diameters (40 and 270 nm) and 15 μm length has been investigated for low-energy electrons (2–120 eV). The total intensity of transmitted current weakly depends on the incident electron energy and tilt angle defined with respect to the capillary axis. On the other hand, the intensity of elastically transmitted electrons significantly varies with the alteration of electron energy and tilt angle. In addition, we measured an energy distribution of electrons transmitted both in the straightforward direction and at large tilt angle. The measured spectra show that inelastic processes dominate and, in particular, a large amount of low-energy electrons. These low-energy electrons can be either inelastically scattered projectiles or secondary electrons emitted within the capillaries. Furthermore, a change of the tilt angle appears to influence significantly only the intensity of the elastic transmission. The present results suggest a more complex nature of low-energy electron transport through insulating nanocapillaries than proposed for positive ions.

Large-amplitude water waves on deep water have long been known in the seafaring community, and are the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar measurements, well established within the scientific community. There are a number of important models and approaches for the theoretical description of such waves. By analyzing the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled non-linear Schrödinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle θ_c of the direction of the interacting waves, below which all wave systems evolve and display statistics similar to a wave system of non-interacting waves. The results equally apply to other systems described by the non-linear Schrödinger equations, and should be of interest when designing optical wave guides.

We study the nucleation, spreading, and control of irreversible diffusive damage in a 2D fixed-radius random network. The control is achieved via strategic self-destruction. Our studies suggest that rapidly activated aggressive and encompassing self-destruction may provide optimum long-term survival of the network. When the damaged area is sufficiently small, strategic self-destruction may be too dependent on local geometry and the details of the dynamics and hence non-trivial to estimate. Our results reveal broad insights into how it may be possible to combat and control the spreading of problematic effects across fixed-radius random networks.

Raising the potential of a charged hemispherical soap bubble over a critical limit causes deformation of the bubble into a cone and ejection of a charged liquid jet. This is followed by a mode which has not previously been observed in bubbles, in which a long cylindrical liquid film column is created and collapses due to a Rayleigh-Plateau instability creating child bubbles. We show that the formation of the column and subsequent creation of child bubbles is due to a drop in potential caused by the ejection of charge from the system via the jet. Similar dynamics may occur in microscopic charged liquid droplets (electrospray processes), causing the creation of daughter droplets and long liquid spindles.

We discuss thermal convection in the infinite Prandtl number limit. This is relevant for convection in planetary interiors, where inertia of momentum is neglegible, i.e., the Reynolds number of the flow is zero. By means of a numerical two-dimensional model of Rayleigh-Bénard convection, we investigate the evolution of a flow at the Rayleigh number (Ra=10⁸) and demonstrate that even in this zero Reynolds number limit convection exhibits key features of turbulent flow, commonly addressed to high Reynolds number convection. Special attention is given to the phenomenon of reversals in the orientation of the underlying large-scale circulation of the flow. Our case study indicates that flow reversals are an intrinsic feature of turbulent thermal convection resulting from competing states whose main modes turn out to be solutions of the underlying stationary equations.

It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can be made compliant with a pseudo-free-energy principle by simple addition of a gradient force, whose expression is uniquely specified in terms of the fluid density. This additional term is numerically simulated and shown to provide fairly negligible effects on the system evolution during phase-separation. To the best of our knowledge, these important properties of the SC model were not noted before. The approach developed in the present work is based on a continuum analysis: Further extensions, more in line with a discrete lattice theory (Shan X., Phys. Rev. E, 77 (2008) 066702), can be envisaged for the future.

Substrate defects crucially influence the onset of sliding drop motion under lateral driving. A finite force is necessary to overcome the pinning influence even of microscale heterogeneities. The depinning dynamics of three-dimensional drops is studied for hydrophilic and hydrophobic wettability defects using a long-wave evolution equation for the film thickness profile. The model is studied employing effective algorithms for the parameter continuation of pinned steady drops and for the time simulation of the dynamics of sliding drops that perform a stick-slip motion. The discussion focuses on common features and significant differences of the depinning process for three-dimensional and two-dimensional drops.

It has recently been shown that a Yaglom law for electrostatic turbulence, that is, a relation for the third-order mixed moment involving the particle number density as a passive scalar and the E×B drift velocity, can be deduced from a simple model of electrostatic fluctuations, which describes bursty turbulence in plasmas. In this letter, the existence of the Yaglom law for electrostatic turbulence in laboratory magnetized plasmas is reported for the first time. Using measurements of intermittent transport at the edge of the RFX-mod reversed field pinch plasma device, we found that the above scaling relation is nicely verified at intermediate scales of few centimeters. In this range of scales, that unambiguously represents the inertial range of electrostatic turbulence, we also analyze the intermittency properties of electrostatic turbulence by measuring anomalous scaling exponents of density and velocity structure functions.

Mutual uncrossability of polymers generates topological constraints on their conformations and dynamics, which are generally described using the tube model. We imaged confinement tubes for individual polymers within a F-actin solution by sampling over many successive micrographs of fluorescently labeled probe filaments. The resulting average tube width shows the predicted scaling behavior. Unexpectedly, we found an exponential distribution of tube curvatures which is attributed to transient entropic trapping in network void spaces.

We consider a mixture of a superfluid Fermi gas of ultracold atoms and a Bose-Einstein condensate of molecules possessing a continuous U(1) (relative phase) symmetry. We study the effects of a spatially random photo-associative–dissociative symmetry-breaking coupling of the systems. Such coupling allows one to control the relative phase between a superfluid order parameter of the Fermi system and the condensate wave function of molecules for temperatures below the Bardeen-Cooper-Schriefer critical temperature. The presented mechanism of phase control belongs to the general class of phenomena in which disorder interacts with continuous symmetry. Our results show the robustness and wide range of applicability of disorder-induced order and are valid for both disordered and regular couplings. Here, the effect is studied in the case of interacting fermionic and bosonic gases in the superfluid phase.

As semiconductor devices shrink in size, the challenge of characterisation of their dopant distributions intensifies. Scanning electron microscopy (SEM) has been proposed as a suitable technique to overcome this challenge. However, current low-voltage (LV) SEMs are incapable of the probe sizes required for nano-scale dopant mapping, but the recently commercialised helium ion microscope (HeIM) is capable of probe sizes of 0.25 nm; a significant improvement over LVSEM. This paper discusses the dopant contrast mechanism in the HeIM and is the first demonstration of nano-scale, quantitative dopant mapping in the HeIM.

We have studied the structural and superconducting properties of β–FeSe under pressures up to 26 GPa using synchrotron radiation and diamond anvil cells. The bulk modulus of the tetragonal phase is 28.5(3) GPa, much smaller than the rest of Fe based superconductors. At 12 GPa we observe a phase transition from the tetragonal to an orthorhombic symmetry. The high-pressure orthorhombic phase has a higher T_c reaching 34 K at 22 GPa.

We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field.

The field-induced switching of conductance in the charge ordered half-doped manganites is controlled by the combination of metastability, an inhomogeneous high-field state, and cation disorder. We study this non-equilibrium problem via real space Monte Carlo on a disordered strong coupling model appropriate to the manganites. We reproduce the variation of the switching fields with the mean ionic radius r_A and cation disorder σ_A, and demonstrate how the experimental features arise from the proximity of several phases in the Landau free-energy landscape. Our prediction for the field melted state is consistent with a growing body of experimental evidence.

Magnetic-field dependence of the ac impedance Z(f,H)=R(f,H)+jX(f, H) in La_0.67Ba_0.33MnO₃ carried out over a wide frequency range (f=0 to 30 MHz) reveals a huge low-field ac magnetoresistance, ΔR/R=-55% at f=15 MHz and magnetoreactance, ΔX/X=-80% at f=3 MHz in μ₀H=100 mT at room temperature. We show contrasting evolution of ΔR/R and ΔX/X with increasing magnetic field and frequency. While ΔR/R is negative and shows a single peak at μ₀H=0 T for all but f=30 MHz, the single peak in ΔX/X transforms into a valley at the origin and a double peak at H=±H_k which shifts upward in H with increasing frequency. The ΔX/X eventually changes sign from negative to positive above 25 MHz. The observed features in ΔX/X suggest possible occurrence of ferromagnetic resonance in MHz range.

Performing an analysis within density functional theory, we develop insight into the structural and electronic properties of the oxide heterostructure LaAlO₃/SrTiO₃. Electrostatic surface effects are decomposed from the internal lattice distortion in order to clarify their interplay. We first study the interface relaxation by a multi-layer system without surface, and the surface effects, separately, by a substrate-film system. While elongation of the TiO₆ octahedra at the interface enhances the metallicity, reduction of the film thickness has the opposite effect due to a growing charge depletion. The interplay of these two effects, as reflected by the full lattice relaxation in the substrate-film system, however, strongly depends on the film thickness. An inversion of the TiO₆ distortion pattern for films thinner than four LaAlO₃ layers results in an insulating state.

For further improvement of magnetic information storage density and writing speed, laser-induced writing procedures have been extensively explored recently. Within the framework of the Landau-Lifshitz-Bloch equation of motion, which does not conserve the length of the magnetization vector, we investigate thermally assisted switching analytically. We show that for temperatures close to (but still below) the Curie temperature two reversal modes appear, an elliptical mode and a linear one. We calculate the coercive fields and energy barriers for both elliptical and linear switching. Investigating the dynamics of linear reversal, which is the more relevant case close to the Curie temperature, we calculate the temperature dependence of the minimal time and field needed for thermally assisted switching below and above the Curie temperature.

We show that the strong Nernst signal observed recently in amorphous superconducting films far above the critical temperature is caused by the fluctuations of the superconducting order parameter. We demonstrate a striking agreement between our theoretical calculations and the experimental data at various temperatures and magnetic fields. Besides, the Nernst effect is interesting not only in the context of superconductivity. We discuss some subtle issues in the theoretical study of thermal phenomena that we have encountered while calculating the Nernst coefficient. In particular, we explain how the Nernst theorem (the third law of thermodynamics) imposes a strict constraint on the magnitude of the Nernst effect.

We consider the rupture dynamics of a homopolymer chain pulled at one end at a constant loading rate. Our model of the breakable polymer is related to the Rouse chain, with the only difference that the interaction between the monomers is described by the Morse potential instead of the harmonic one, and thus allows for mechanical failure. We show that in the experimentally relevant domain of parameters the dependence of the most probable rupture force on the chain length may be non-monotonic, so that the medium-length chains break easier than the short and the long ones. The qualitative theory of the effect is presented.

The phase diagram of Yukawa particles confined between two parallel hard walls is calculated at zero temperature beyond the bilayer regime by lattice-sum-minimization. Tuning the screening, a rich phase behavior is found in the regime bounded by stable two triangular layers and three square layers. In this regime, alternating prism phases with square and triangular basis, structures derived from a hcp bulk lattice, and a structure with two outer layers and two inner staggered rectangular layers, reminiscent of a Belgian waffle iron, are stable. These structures are verifiable in experiments on charged colloidal suspensions and dusty plasma sheets.

Motivated by widely observed examples in nature, society and software, where groups of related nodes arrive together and attach to existing networks, we consider network growth via sequential attachment of linked node groups or graphlets. We analyze the simplest case, attachment of the three node -graphlet, where, with probability α, we attach a peripheral node of the graphlet, and with probability (1-α), we attach the central node. Our analytical results and simulations show that tuning α produces a wide range in degree distribution and degree assortativity, achieving assortativity values that capture a diverse set of many real-world systems. We introduce a fifteen-dimensional attribute vector derived from seven well-known network properties, which enables comprehensive comparison between any two networks. Principal Component Analysis of this attribute vector space shows a significantly larger coverage potential of real-world network properties by a simple extension of the above model when compared against a classic model of network growth.

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this unduely constrains their results, leading to a bias in the size of the communities they find and limiting their effectiveness. To solve this problem, we propose adding a step, which is a modification of the Kernighan-Lin algorithm, to the existing algorithms. This additional step does not increase the order of their computational complexity. We show that, if this step is combined with a commonly used method, the identified constraint and resulting bias are removed, and its ability to find the optimal partitioning is improved. The effectiveness of this combined algorithm is also demonstrated by using it on real-world example networks. For a number of these examples, it achieves the best results of any known algorithm.

We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied to sets of graphs that have as links different sets of interactions among the system's elements, which are described as network nodes. It can also be applied to correlation-based graphs, where the links are weighted and represent the correlation strength between all pairs of nodes. We applied this method to the European scientific collaboration network, which is composed of all the projects supported by the European Framework Program FP6, and also to the correlation-based network of the 100 highest capitalized stocks traded in the New York Stock Exchange. For both cases we identified meaningful structures, such as a strongly interconnected community of countries that play an important role in the collaboration network, and clusters of stocks belonging to different sectors of economic activity, which gives significant information about the investigated systems.

One-dimensional Si nanostructures, grown on a Ag(110) substrate, have been used as a template to grow Co nanolines. Before Co deposition, the self-assembled Si nanostripes were characterized by high-resolution scanning tunneling microscopy. From this, an original atomic arrangement of silicon adatoms forming nanostripes can be proposed. The early stages of the Co deposition at room temperature on the Si nanostripes have then been studied by scanning tunneling microscopy, enabling the localization of adsorbed Co atoms. We show that Co is adsorbed on top of the Si nanostripes forming nanolines. No Co adsorption was detected on the pure Ag-surface in between the stripes. The preparation of an interesting one-dimensional Co-Si nanosystem is demonstrated.

The influence of an underlying current on three-wave interactions of capillary water waves is studied. The fact that in irrotational flow resonant three-wave interactions are not possible can be invalidated by the presence of an underlying current of constant non-zero vorticity. We show that: 1) wave trains in flows with constant non-zero vorticity are possible only for two-dimensional flows, 2) only positive constant vorticities can trigger the appearance of three-wave resonances, 3) the number of positive constant vorticities which do trigger a resonance is countable and 4) the magnitude of a positive constant vorticity triggering a resonance cannot be too small.

The properties of geodesics flow are studied in a Friedmann-Robertson-Walker metric perturbed due to the inhomogeneities of matter. The basic, averaged Jacobi equation is derived, which reveals that the low-density regions (voids) are able to induce hyperbolicity, even if the global curvature of the Universe is zero or slightly positive. It is shown that the energy independence is a characteristic property of these geometric effects. The importance of these conclusions is determined by the temperature independent ellipticity of excursion sets and regions of different randomness found in Kolmogorov Cosmic Microwave Background (CMB) maps.