Cusps in KL→3π decays

The pronounced cusp in K→3π decays which is generated by the pion mass difference is directly related to the ππS-wave scattering lengths. We apply a nonrelativistic effective field theory framework to evaluate the amplitudes for K_L→3π decays in a systematic manner. Electromagnetic effects in the neutral channel K_L→3π⁰ are also discussed.     

Study of classical mechanical systems with complex potentials

We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature — the closed orbits become open ones.     

Universality in bibliometrics

Many discussions have enlarged the literature in Bibliometrics since the Hirsch proposal, the so called h-index. Ranking papers according to their citations, this index quantifies a researcher only by its greatest possible number of papers that are cited at least h times. A closed formula for h-index distribution that can be applied for distinct databases is not yet known. In fact, to obtain such distribution, the knowledge of citation distribution of the authors and its specificities are required. Instead of dealing with researchers randomly chosen, here we address different groups based on distinct databases. The first group is composed of physicists and biologists, with data extracted from Institute of Scientific Information (ISI). The second group is composed of computer scientists, in which data were extracted from Google-Scholar system. In this paper, we obtain a general formula for the h-index probability density function (pdf) for groups of authors by using generalized exponentials in the context of escort probability. Our analysis includes the use of several statistical methods to estimate the necessary parameters. Also an exhaustive comparison among the possible candidate distributions are used to describe the way the citations are distributed among authors. The h-index pdf should be used to classify groups of researchers from a quantitative point of view, which is meaningfully interesting to eliminate obscure qualitative methods.     

Josephson effect in supercondutor/ferromagnetic semiconductor/superconductor junctions

Using a general expression for dc Josephson current, we study the Josephson effect in ballistic superconductor (SC)/ferromagnetic semiconductor (FS)/SC junctions, in which the mismatches of the effective mass and Fermi velocity between the FS and SC, spin polarization P in the FS, as well as strengths of potential scattering Z at the interfaces are included. It is shown that in the coherent regime, the oscillatory dependences of the maximum Josephson current on the FS layer thickness L and Josephson current on the macroscopic phase difference φ for the heavy and light holes, resulting from the spin splitting energy gained or lost by a quasiparticle Andreev-reflected at the FS/SC interface, are much different due to the different mismatches in the effective mass and Fermi velocity between the FS and the SC, which is related to the crossovers between positive (0) and negative (π) couplings or equivalently 0 and π junctions. Also, we find that, for the same reason, Z and P are required not to surpass different critical values for the Josephson currents of the heavy and light holes. Furthermore, it is found that, for the dependence of the Josephson current on φ, regardless of how L,Z, and P change, the Josephson junctions do not transit between 0 and π junctions for the light hole.     

Influence of surface heterogeneity in electroosmotic flows—Implications in chromatography, fluid mixing, and chemical reactions in microdevices

We analyze the influence of surface heterogeneity, inducing a random ζ-potential at the walls in electroosmotic incompressible flows. Specifically, we focus on how surface heterogeneity modifies the physico-chemical processes (transport, chemical reaction, mixing) occurring in microchannel and microreactors. While the macroscopic short-time features associated with solute transport (e.g. chromatographic patterns) do not depend significantly on ζ-potential heterogeneity, spatial randomness in the surface ζ-potential modifies the spectral properties of the advection-diffusion operator, determining different long-term properties of transport/reaction phenomena compared to the homogeneous case. Examples of physical relevance (chromatography, infinitely fast reactions) are addressed.     

The Gaussian effective potential and stochastic partial differential equations

We investigate arbitrary stochastic partial differential equations subject to translation invariant and temporally white noise correlations from a nonperturbative framework. The method that we expose first casts the stochastic equations into a functional integral form, then it makes use of the Gaussian effective potential approach, which is an useful tool for describing symmetry breaking. We apply this method to the Kardar-Parisi-Zhang equation and find that the system exhibits spontaneous symmetry breaking in and (3+1) Euclidean dimensions, providing insight into the evolution of the system configuration due to the presence of noise correlations. A simple and systematic approach to the renormalization, without explicit regularization, is employed.     

Frequency-dependent linear and non-linear response properties of single carrier quantum dots: Role of effective mass and anharmonicity in the confinement potential

We explore the pattern of frequency-dependent linear and non-linear optical (NLO) response of one electron quantum dots harmonically confined in two dimensions. For some fixed values of transverse magnetic field strength (ω_c), and harmonic confinement potential (ω₀), the influence of effective mass (m^*) of the system and the symmetry breaking anharmonic interaction on the frequency-dependent linear (α), and the first (β), and second (γ) NLO responses of the dot is computed through linear variational route. The investigation reveals interesting roles played by the anharmonic interaction and effective mass in modulating the response properties.     

Information theoretic description of networks

We present a new information theoretic approach for network characterizations. It is developed to describe the general type of networks with n nodes and L directed and weighted links, i.e., it also works for the simpler undirected and unweighted networks. The new information theoretic measures for network characterizations are based on a transmitter-receiver analogy of effluxes and influxes. Based on these measures, we classify networks as either complex or non-complex and as either democracy or dictatorship networks. Directed networks, in particular, are furthermore classified as either information spreading and information collecting networks.The complexity classification is based on the information theoretic network complexity measure medium articulation (MA). It is proven that special networks with a medium number of links (L∼n^1.5) show the theoretical maximum complexity . A network is complex if its MA is larger than the average MA of appropriately randomized networks: MA>MA_r. A network is of the democracy type if its redundancy R<R_r, otherwise it is a dictatorship network. In democracy networks all nodes are, on average, of similar importance, whereas in dictatorship networks some nodes play distinguished roles in network functioning. In other words, democracy networks are characterized by cycling of information (or mass, or energy), while in dictatorship networks there is a straight through-flow from sources to sinks. The classification of directed networks into information spreading and information collecting networks is based on the conditional entropies of the considered networks (H(A/B)=uncertainty of sender node if receiver node is known, H(B/A)=uncertainty of receiver node if sender node is known): if H(A/B)>H(B/A), it is an information collecting network, otherwise an information spreading network.Finally, different real networks (directed and undirected, weighted and unweighted) are classified according to our general scheme.     

Ground-state properties of the one-dimensional extended Hubbard model at half filling

The density-matrix renormalization group (DMRG) technique is used to study the ground-state properties of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t. We calculate the static spin structure factor to consider the spin degrees of freedom. We notice a striking difference of the static spin structure factor among the spin-density-wave, charge-density-wave (CDW), and bond-order-wave (BOW) phases. Based on the results, we identify the BOW-CDW transition at small (large) U value as continuous (of first order). We also calculate the double occupancy to consider the charge degrees of freedom. For large U, the double occupancy show a discontinuous jump at the BOW-CDW critical point and it implies first-order transition. With decreasing U, the jump becomes smaller and vanishes at the tricritical point U_t≈5.961t. This value is close to our previous estimation U_t=5.89t obtained with other quantities. Consequently, the results of static spin structure factor and double occupancy support the accuracy of our ground-state phase diagram.     

Anti-persistence in levels of Lake Naivasha: Assessing effect of human intervention through time-series analysis

Lake Naivasha in Kenya is an important natural fresh water reserve, supporting surrounding wildlife as well as agriculture and industry. Uncontrolled use of the lake water for the past few decades is causing concern for environmentalists. In the present paper, fluctuations in the lake level for the last half century are analysed using standard tools for time-series analysis. The intervals 1951-1980 (period I) and 1981-2000 (period II) are treated separately, to look for any difference in their statistical patterns. From period II onwards, increased human consumption is believed to affect the level significantly. We analyse the data using three different approaches: (i) rescaled range analysis (R/S), (ii) roughness scaling analysis and (iii) a Lomb periodogram. R/S analysis shows no difference between the behavior in periods I and II, but the other methods reveal different fluctuation patterns for the two periods. The water level shows stronger fluctuations in period I compared to II. R/S analysis, however, shows an interesting anti-persistence with a Hurst exponent 0.44, which is not usually observed in natural time series.     

Pricing European options with a log Student’s t-distribution: A Gosset formula

The distributions of returns for stocks are not well described by a normal probability density function (pdf). Student’s t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student’s t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.     

Deterministic and random partially self-avoiding walks in random media

Consider a set of N cities randomly distributed in the bulk of a hypercube with d dimensions. A walker, with memory μ, begins his route from a given city of this map and moves, at each discrete time step, to the nearest point, which has not been visited in the preceding μ steps. After reviewing the more interesting general results, we consider one-dimensional disordered media and show that the walker needs not to have full memory of its trajectory to explore the whole system, it suffices to have memory of order lnN/ln2.     

Complex turing patterns in non-linearly coupled systems

Recently pattern formation in layered structures, showing complicated superimposed patterns, has been modeled by coupling two Turing systems linearly, i.e., passively, such that the characteristic length scales of the independent systems are well separated. Here we propose a model of two non-linearly coupled Turing systems to study pattern formation in layered membrane-like structures, where the coupling plays an active role and changes the kinetics of the uncoupled systems. Extensive numerical simulations show that non-linear coupling generates a number of new regular patterns different from the ones observed earlier with linearly coupled systems. Some of them turn out to be superimposed patterns with different length scales, but many are not. Also, contrary to the linear coupling case, the strength of the non-linear coupling is found to play an important role in the formation and selection of patterns.     

Classical limit of the Casimir entropy for scalar massless field

We study the Casimir effect at finite temperature for a massless scalar field in the parallel plates geometry in N spatial dimensions, under various combinations of Dirichlet and Neumann boundary conditions on the plates. We show that in all these cases the entropy, in the limit where energy equipartitioning applies, is a geometrical factor whose sign determines the sign of the Casimir force.     

Contact and phonon scattering effects on quantum transport properties of carbon-nanotube field-effect transistors

We investigated the phonon scattering effects on the transport properties of carbon nanotube devices with micron-order lengths at room temperature, using the time-dependent wave-packet approach based on the Kubo formula within a tight-binding approximation. We studied the scattering effects of both the longitudinal acoustic and the optical phonons on the transport properties. The conductance of semiconducting nanotubes is decreased by the acoustic phonon, instead of the optical phonon. Furthermore, we clarified how the electron mobilities of the devices are affected by the acoustic phonon.     

Kinetic and mass mixing with three abelian groups

We present the possible mixing effects associated with the low-energy limit of a Standard-Model extension by two abelian gauge groups U₁(1)×U₂(1). We derive general formulae and approximate expressions that connect the gauge eigenstates to the mass eigenstates. Applications using the well-studied groups UB(1), U(1)_B−L, U(1)_Lα−Lβ (Lα being lepton flavor numbers), and UDM(1) (a symmetry acting only on the dark matter sector) are discussed briefly.     

The non-perturbative renormalization group in the ordered phase

We study some analytical properties of the solutions of the non-perturbative renormalization group flow equations for a scalar field theory with Z₂ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility χ(M) at M=±M₀ (M₀ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we stress that these conditions are not satisfied by a sharp cut-off in dimensions of space d<4.By generalizing a method proposed earlier by Bonanno and Lacagnina [Nucl. Phys. B 693 (2004) 36] to any kind of cut-off we propose to solve numerically the renormalization group flow equations for the threshold functions rather than for the local potential. It yields an algorithm sufficiently robust and precise to extract universal as well as non-universal quantities from numerical experiments at any temperature, in particular at sub-critical temperatures in the ordered phase. Numerical results obtained for the φ⁴ potential with three different cut-off functions are reported and compared. The data confirm our theoretical predictions concerning the analytical behavior of χ(M) at M=±M₀.Fixed point solutions of the adimensioned renormalization group flow equations are also obtained in the same vein, that is by solving the fixed points equations and the associated eigenvalue problem for the threshold functions rather than for the potential. We report high precision data for the odd and even spectra of critical exponents for different cut-offs obtained in this way.     

Nonlinear statistical coupling

By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Q=1−q defined as the degree of nonlinear coupling between the statistical states. Positive values of Q have coupled statistical states, a larger entropy metric, and a maximum coupled-entropy distribution of compact-support coupled-Gaussians. Negative values of Q have decoupled statistical states and for −2<Q<0 a maximum coupled-entropy distribution of heavy-tail coupled-Gaussians. The conjugate transformation between the heavy-tail and compact-support domains is shown to be for coupled-Gaussian distributions. This conjugate relationship has been used to extend the generalized Fourier transform to the compact-support domain and to define a scale-invariant correlation structure with heavy-tail limit distribution. In the present paper, we show that the conjugate is a mapping between the source of nonlinearity in non-stationary stochastic processes and the nonlinear coupling which defines the coupled-Gaussian limit distribution. The effects of additive and multiplicative noise are shown to be separable into the coupled-variance and the coupling parameter Q, providing further evidence of the importance of the generalized moments.     

Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients

We explore the generalization of the ordinary multinomial coefficient, based on the deformed q-multiplication and q-division. Aim of this study is to construct the appropriate multinomial coefficients, from which one can obtain the Tsallis, Rényi and nonextensive Gaussian entropy, respectively. We show that for all three above entropies there are two possible ways to define the generalized multinomial coefficient. Its consequence is discussed.     

Simulation of a spintronic transistor: A study of its performance

We study theoretically the magnetic bipolar transistor, and compare its performance with common bipolar transistor. We present not only the simulation results for the characteristic curves, but also other relevant parameters related with its performance, such as: the current amplification factor, the open-loop gain, the hybrid parameters and the cutoff frequency. We noted that the spin-charge coupling introduces new phenomena that enrich the functionality characteristics of the magnetic bipolar transistor. Among other things, it has an adjustable band structure, which may be modified during the device operation; it exhibits the already known spin-voltaic effect. On the other hand, we observed that it is necessary a large g-factor to analyze the influence of the field B over the transistor. Nevertheless, we consider the magnetic bipolar transistor as a promising device for spintronic applications.