Showing papers in "European Physical Journal B in 2003"

Economic Small-World Behavior in Weighted Networks

Abstract: The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation is valid only for topological networks. In this paper we propose a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are “cheap” to build, and nevertheless efficient in propagating information, both at global and local scale. In this way we provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are studied, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems.

Fractional ac Josephson effect in p- and d-wave superconductors

Abstract: For certain orientations of Josephson junctions between two px-wave or two d-wave superconductors, the subgap Andreev bound states produce a \(4\pi\)-periodic relation between the Josephson current I and the phase difference \(\phi\): \(I\propto\sin(\phi/2)\) Consequently, the ac Josephson current has the fractional frequency \(eV/\hbar\), where V is the dc voltage In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction We also study junctions between singlet s-wave and triplet px-wave, as well as between chiral \(p_x\pm ip_y\)-wave superconductors

Self-energy-functional approach to systems of correlated electrons

Abstract: The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a certain reference system. The variational scheme allows to construct new non-perturbative and thermodynamically consistent approximations. Numerical results illustrate the practicability of the method.

Analytical results for the Sznajd model of opinion formation

Abstract: The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed 1/n dependence in the distribution of votes in Brazilian elections is provided.

Fluorescence of a dye-doped cholesteric liquid crystal film in the region of the stop band: theory and experiment

Abstract: Due to the sinusoidal modulation of the dielectric properties along the helical axis, cholesteric liquid crystals exhibit a photonic stop band for circularly polarized light, which strongly affects the emission of fluorescent guest molecules. In this paper, we discuss the resulting changes in the emission spectrum. In an analytical treatment, we first derive the photonic densities of states of the two normal light modes for propagation parallel to the helical axis, taking into account multiple reflections due to the finite film thickness. Then we discuss the influence of the degree of order of the dye's transition dipole moment on the emission characteristics. Finally, we present experimental results, which show excellent quantitative agreement with our theoretical description.

Giant entropy change at the co-occurrence of structural and magnetic transitions in the Ni2.19Mn0.81Ga Heusler alloy

Abstract: We have studied the isothermal entropy change around a first-order structural transformation and in correspondence to the second-order Curie transition in the ferromagnetic Heusler alloy Ni2.15Mn0.85Ga. The results have been compared with those obtained for the composition Ni2.19Mn0.81Ga, in which the martensitic structural transformation and the magnetic transition occur simultaneously. With a magnetic field span from 0 to 1.6 T, the magnetic entropy change reaches the value of 20 J/kg K when transitions are co-occurring, while 5 J/kg K is found when the only structural transition occurs.

On the nature of the low-temperature phase in discontinuous mean-field spin glasses

Abstract: The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking (1RSB) ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry breaking (FRSB) phase, is often regarded as an inessential, and somehow exotic phenomenon. In this paper we show that the metastable states which are relevant for the out-of-equilibrium dynamics of such systems are always in a FRSB phase. The only exceptions are (to the best of our knowledge) the p-spin spherical model and the random energy model (REM). We also discuss the consequences of our results for aging dynamics and for local search algorithms in hard combinatorial problems.

Bubbles, crashes and intermittency in agent based market models

Abstract: We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the possibility of not participating to the market. The price is updated according to the excess demand, and the wealth of the agents is properly accounted for. Only two parameters play a significant role: one describes the impact of trading on the price, and the other describes the propensity of agents to be trend following or contrarian. We observe three different regimes, depending on the value of these two parameters: an oscillating phase with bubbles and crashes, an intermittent phase and a stable `rational' market phase. The statistics of price changes in the intermittent phase resembles that of real price changes, with small linear correlations, fat tails and long range volatility clustering. We discuss how the time dependence of these two parameters spontaneously drives the system in the intermittent region. We analyze quantitatively the temporal correlation of activity in the intermittent phase, and show that the `random time strategy shift' mechanism that we proposed earlier allows one to understand the observed long ranged correlations. Other mechanisms leading to long ranged correlations are also reviewed. We discuss several other issues, such as the formation of bubbles and crashes, the influence of transaction costs and the distribution of agents wealth.

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition

Abstract: The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a mean-field approach which is interesting conceptually: Trial self-energies from a two-site single-impurity Anderson model are used to evaluate an exact and general variational principle. While this restriction of the domain of the functional represents a strong approximation, the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the “linearized DMFT” which has been suggested previously as a handy approach to study the critical regime close to the transition. It turns out that the two-site approximation is able to reproduce the complete (zero and finite-temperature) phase diagram for the Mott transition. For the critical point at T = 0, the entire calculation can be done analytically. This calculation elucidates different general aspects of the self-energy-functional theory. Furthermore, it is shown how to deal with a number of technical difficulties which appear when the self-energy functional is evaluated in practice.

Glass models on Bethe lattices

Abstract: We consider “lattice glass models” in which each site can be occupied by at most one particle, and any particle may have at most l occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase diagram, with a particular focus on the vitreous phase and the highest packing limit. We also study the energy landscape via the configurational entropy, and discuss different equilibrium glassy phases. Finally, we show that a kinetic freezing, depending on the particular dynamical rules chosen for the model, can prevent the equilibrium glass transitions.

Full counting statistics of a general quantum mechanical variable

Abstract: We present a quantum mechanical framework for defining the statistics of measurements of \(\int dt \hat{A}(t)\), A(t) being a quantum mechanical variable This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device In this way we are able to resolve inconsistencies that occur in earlier definitions We suggest two schemes to observe the so defined statistics experimentally

Efficient Hopfield pattern recognition on a scale-free neural network

Abstract: Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N2 bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N2. The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabasi-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q 3. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time.

Engineering decoherence in Josephson persistent-current qubits - Measurement apparatus and other electromagnetic environments

Abstract: We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the spectral density of the bosonic bath can be derived from the electromagnetic impedance that is coupled to the qubit. Part of the electromagnetic environment is a measurement apparatus (DC-SQUID), that is permanently coupled to the single quantum system that is studied. Since there is an obvious conflict between long coherence times and an efficient measurement scheme, the measurement process is analyzed in detail for different measurement schemes. We show, that the coupling of the measurement apparatus to the qubit can be controlled in situ. Parameters that can be realized in experiments today are used for a quantitative evaluation, and it is shown that the relaxation and dephasing rates that are induced by the measurement setup can be made low enough for a time-resolved study of the quantum dynamics of Josephson persistent-current qubits. Our results can be generalized as engineering rules for the read-out of related qubit systems.

Broad distribution effects in sums of lognormal random variables

Abstract: The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out.

3D Large scale Marangoni convection in liquid films

Abstract: We study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. The work is based on the thin film equation which can be derived from the basic hydrodynamic equations. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic fluid parameters.

Crystallographic and magnetic structure of ZnV $\mathsf{_2}$ O $\mathsf{_4}$

Abstract: We report on the crystallographic and magnetic structure of the geometrically frustrated spinel ZnV2O4 as determined by neutron powder diffraction At T = 51 K, a cubic-to-tetragonal phase transition takes place The low temperature crystallographic structure is characterized by the space group I41/amd and unit cell dimensions \({a/\sqrt{2} \times a/\sqrt{2} \times a}\) with a being the lattice constant of the cubic phase The corresponding antiferromagnetic structure of the vanadium sublattice can be described by a propagation vector \({{\bf k} = (001)}\) with the magnetic moments being aligned parallel to the c-axis The ordered magnetic moment is 065(5) \({\mu_B}\) per V3+ ion The experimental results are in accord with recent theoretical models proposing spin-driven Jahn-Teller distortions The results are also compared with reports on non-ordering ZnV2O4

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

Abstract: A numerical study of the magnetic induction equation has been performed on von Karman type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Karman sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.

Characterization of anti-phase boundaries in epitaxial magnetite films

Abstract: The occurrence of anti-phase domain boundaries (APBs) in epitaxial Fe3O4 films has a strong influence on the resistivity, magnetic and magneto-resistance properties of these films. It is therefore important to understand the configuration and magnetic coupling across the boundary. We have studied the distribution of shift vectors and the relationship between the shift vector and the boundary plane and the resulting magnetic coupling at the boundary. The vast majority of APBs have $1/4\langle110\rangle$ shifts while those with 1/2[100] shift are very uncommon. Approximately 45% of APBs have shift vectors in the plane of the film. Their boundary plane is perpendicular to the shift vectors and in this case the magnetic coupling can be either ferromagnetic or anti-ferromagnetic. The remaining 55% of APBs have shift vectors out of the film plane, with the boundary planes not perpendicular to the shift vector but close to {100} or {310}, resulting in a ferromagnetic coupling when the boundary plane is {100} and in an anti-ferromagnetic coupling when the boundary plane is {310}.

Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jaynes' principle

Abstract: For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes' principle. It is these states which thermodynamical systems should generically evolve into.

Disease Spreading in Structured Scale-Free Networks

Abstract: We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading.

Fourier's Law confirmed for a class of small quantum systems

Abstract: Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.

Percolation of polyatomic species on a square lattice

Abstract: In this paper, the percolation of (a) linear segments of size k and(b) k-mers of different structures and forms deposited on a square lattice have been studied. In the latter case, site and bond percolation have been examined. The analysis of results obtained by using finite size scaling theory is performed in order to test the universality of the problem by determining the numerical values of the critical exponents of the phase transition occurring in the system. It is also determined that the percolation threshold exhibits a exponentially decreasing function when it is plotted as a function of the k-mer size. The characteristic parameters of that function are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited.

Scale-free behavior of the Internet global performance

Abstract: Measurements and data analysis have proved very effective in the study of the Internet's physical fabric and have shown heterogeneities and statistical fluctuations extending over several orders of magnitude. Here we focus on the relationship between the Round-Trip-Time (RTT) and the geographical distance. We define dimensionless variables that contain information on the quality of Internet connections finding that their probability distributions are characterized by a slow power-law decay signalling the presence of scale-free features. These results point out the extreme heterogeneity of Internet delay since the transmission speed between different points of the network exhibits very large fluctuations. The associated scaling exponents appear to have fairly stable values in different data sets and thus define an invariant characteristic of the Internet that might be used in the future as a benchmark of the overall state of “health” of the Internet.

How accurate can the determination of chiral indices of carbon nanotubes be? An experimental investigation of chiral indices determination on DWNT by electron diffraction

Abstract: We present a general and systematic method for determining the chiral indices of carbon nanotubes. This method relies on the semi-quantitative analysis of experimental selected area diffraction pattern intensities, together with extensive comparison with kinematic theory. We show how to retrieve the chiral indices of single walled or multiwalled carbon nanotubes, even when their radii are large (up to approximately 40 A). All theoretical and experimental sources of errors are discussed. By discussing the experimental case of a double-walled carbon nanotube, we show how it is possible to determine the chiral indices of each of its constituant tubes independently, by analyzing parts of the diffraction pattern where the contributions of these tubes do not interfere. Using the parts where all the contributions do interfere, we successfully crosschecked independently the preceding determination.

A causal multifractal stochastic equation and its statistical properties

Abstract: Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to discrete cascades. Here a causal log-normal stochastic process is introduced; its multifractal properties are demonstrated together with other properties such as the composition rule for scale dependence and stochastic differential equations for time and scale evolutions. This multifractal stochastic process is continuous in scale ratio and in time. It has a simple generating equation and can be used to generate sequentially time series of any length.

Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials

Abstract: The analytic embedded atom method (EAM) type many-body potentials of hcp rare earth metals (Dy, Er, Gd, Ho, Nd, Pr, and Tb) have been constructed. The hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure, and the hcp lattice with ideal c/a. The mechanical stability of the corresponding hcp lattice with respect to large change of density and c/a ratio is examined. The phonon spectra, stacking fault and surface energy are calculated. The activation energy for vacancy diffusion in these metals has been calculated and the most possible diffusion paths are predicted. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the crowdion and basal split are the most stable configurations. The SIA formation energy increases linearly with the increase of the melting temperature.

Melting of ice in porous glass: why water and solvents confined in small pores do not crystallize?

Abstract: The melting of ice in porous glass having different distribution of pores sizes is analyzed in details. One shows that confined water crystallizes only partially and that an interface layer, between the ice crystallites and the surface of the pore, remains liquid. Properties of this non crystalline interface at low temperature is studied by NMR and DSC. Both methods lead to an interface thickness h of the order of 0.5 nm, this explains why water do not crystallize when the dimension of confinement is less than a critical length $d^{*}\sim 1$ nm. The variation of the melting enthalpy per gram of total amount of water with the confinement length is explained taking into account two effects: a) the presence of this layer of water at the interface and b) the linear variation of the melting enthalpy $\Delta H_{m}$ with the melting temperature T m . From the data of the literature one draws the same conclusions concerning other solvents in similar porous materials. Also one points out the important role of the glass temperature T g in preventing the crystallization of the liquids confined in small pores and/or between the crystallites and the surface of the pores.

Evidence for a solid phase of dodecahedral C 20

Abstract: Evidence is presented for the formation of a solid phase based on the smallest fullerene, C20, in thin diamond-like carbon films deposited by ultraviolet laser ablation from diamond onto nickel substrates at room temperature in the presence of 10-4 torr of cyclohexane or benzene. Laser desorption mass spectrometry from the films shows the presence of C20, C21 and C22 species, while micro-Raman spectroscopy and electron diffraction from selected particles together with first principle density-functional calculations, indicate a cubic solid with dodecahedral C20 cages as building blocks. Unlike solid C60 and fully protonated C20, which are bound by van der Waals forces, the proposed structure is stabilized by linking of the C20 dodecahedra with bridging carbon atoms at interstitial tetrahedral sites to form a face-centered-cubic lattice with 22 carbon atoms per unit cell.

Numerical study of two classes of cellular automaton models for traffic flow on a two-lane roadway

Abstract: In this paper, we present computer simulation results of traffic flow on a two-lane roadway with different types of vehicles, cars and trucks for example. We consider two classes of two-lane traffic cellular automaton models, namely the well known Nagel-Schreckenberg model and an extension of the Fukui-Ishibashi model. These two models, which differ in their acceleration limits, show an important differences in their fundamental diagrams, lane-changing and ping-pong behaviors. Moreover, we investigate the importance of braking noise and the proportion of trucks on the traffic flow of a two-lane roadway.

EELS study of interfaces in magnetoresistive LSMO/STO/LSMO tunnel junctions

Abstract: A magnetic tunnel junction consists of two ferromagnetic conducting electrodes separated by an insulating thin layer The performance of such a system strikingly depends on the last conducting atomic layers in contact with the insulator Consequently, the present paper reports a nanoscale electron energy loss spectroscopy (EELS) study, which has been performed across a couple of La066Sr033MnO3,/SrTiO3/La066Sr033MnO3 tunnel junctions with different barrier thickness es (15 nm and 5 nm respectively) It aims at determining not only the chemical composition in the interface areas, but also the effect of the neighbouring atoms on their electronic structure Using recent improvements in the STEM-EELS data acquisition and processing techniques (systematic use of spectrum-line and spectrum-image modes, multivariate statistical analysis, 2D energy deconvolution schemes, etc), the local chemical information is better extracted with shorter acquisition times, while the large increase of the data set contributes to validate the results Within the accuracy level of these measurements, the elemental composition of the different phases remains stable up to the interfaces with no evidence of extra doping Furthermore, weak changes on the Mn-2p edge fine structures (weak shift to lower energy loss values and extra splitting on the top of the Mn L3 line are observed on all the interfaces They are interpreted as a consequence of a slight reduction of the local Mn valence likely accompanied by a strain induced change in local symmetry The discussion is focussed on all spectral changes identified at a (sub)nanometer scale and their potential effects on the degradation of magnetic and transport properties measured, close to room temperature, at a macroscopic level