Proximity effects in a superconductor/ferromagnet junction

A proximity effect in an s-wave superconductor/ferromagnet (SC/F) junction is theoretically studied using the second order perturbation theory for the tunneling Hamiltonian and Green's function method. We calculate a pair amplitude induced by the proximity effect in a weak ferromagnetic metal (FM) and a half-metal (HM). In the SC/FM junction, it is found that a spin-singlet pair amplitude (Ψ_s) and spin-triplet pair amplitude (Ψ_t) are induced in FM and both amplitudes depend on the frequency in the Matsubara representation. Ψ_s is an even function and Ψ_t is an odd function with respect to the Matsubara frequency (ω_n). In the SC/HM junction, we examine the proximity effects by taking account of magnon excitations in HM. It is found that the triplet-pair correlation is induced in HM. The induced pair amplitude in HM shows a damped oscillation as a function of the position and contains the terms of even and odd functions of ω_n as in the case of the SC/FM junction. We discuss that in our tunneling model the pair amplitude of even function of ω_n only contributes to a Josephson current.     

Effective action for strongly correlated electron systems

The su(2|1) coherent-state path-integral representation of the partition function of the t-J model of strongly correlated electrons is derived at finite doping. The emergent effective action is compared to the one proposed earlier on phenomenological grounds by Shankar to describe holes in an antiferromagnet [R. Shankar, Nucl. Phys. B 330 (1990) 433]. The t-J model effective action is found to have an important “extra” factor with no analogue in Shankar?s action. It represents the local constraint of no double electron occupancy and reflects the rearrangement of the underlying phase-space manifold due to the presence of strong electron correlation. This important ingredient is shown to be essential to describe the physics of strongly correlated electron systems.     

Partial equivalence of statistical ensembles and kinetic energy

The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a nontrivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes.     

Modal series solution for an epidemic model

In this article, we generalize a recently proposed method to obtain an exact general solution for the classical Susceptible, Infected, Recovered and Susceptible (SIRS) epidemic mathematical model. This generalization is based upon the nonlinear coupling of two frequencies in an infinite modal series solution. It is shown that these series provide a nonstandard approach in order to obtain an accurate analytical solution for the classical SIRS epidemic model. Numerical results of the SIRS epidemic model for real and complex frequencies are included in order to test the validity and reliability of the method. This method could be applied to a wide class of models in physics, chemistry or engineering.     

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.     

Analytical results of the generalized mean-field theory for diluted magnetic semiconductors with RKKY interaction

Analytical results have been obtained in the framework of the generalized mean-field theory for diluted semiconductors with RKKY interaction. That theory accounts for the non-equivalency of different lattice sites by introducing the distribution function of local effective magnetic fields for non-regular (random) systems with magnetic interaction. The procedure is described that permits to deduce the analytical expression for that function. Corresponding improvement of the traditional mean-field theory could be observed by comparing results of such a generalized analytical model with exact results known for some simple cases, with numerical results of different authors considering the disorder of magnetic impurities’ arrangement, and with experimental data, as well.     

On the quantum dynamics of a point particle in conical space

A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a δ-function potential, which appear naturally in the model. These pathological potentials are treated with the self-adjoint extension method which yields the correct boundary condition (not necessarily a null wavefunction) at the origin. We show that the usual boundary condition requiring that the wavefunction vanishes at the origin is arbitrary and drastically reduces the number of bound states if used. The situation studied here is closely related to the problem of a dipole moving in conical space.     

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.     

A generalization of the Virasoro algebra to arbitrary dimensions

Colored tensor models generalize matrix models in higher dimensions. They admit a 1/N expansion dominated by spherical topologies and exhibit a critical behavior strongly reminiscent of matrix models. In this paper we generalize the colored tensor models to colored models with generic interaction, derive the Schwinger Dyson equations in the large N limit and analyze the associated algebra of constraints satisfied at leading order by the partition function. We show that the constraints form a Lie algebra (indexed by trees) yielding a generalization of the Virasoro algebra in arbitrary dimensions.     

Variational approach to strong correlation in the photoemission of electron-doped superconductors

We use a variational approach with strictly strong-correlated constraint to gain insight into low-energy states of t-t^′-t^″-J model in the electron-doped regime. Compared with the recent results on the electron-doped cuprates obtained by angle-resolved photoemission spectroscopy (ARPES), we show that based on the long-range ordered antiferromagnetic metallic state prohibiting vacant sites, our results lead to qualitatively similar trends in ARPES spectra and Fermi surface topology. Additionally, the results about the evolution of the energy gap and spectral weight as a function of doping will be discussed.     

Variational treatment of Faraday waves in inhomogeneous Bose-Einstein condensates

Motivated by the recent experimental progress on the collective modes of a Bose-Einstein condensate whose atomic scattering length is tuned via Feshbach resonances, we analyze by variational means the dynamics of Faraday waves in trapped Bose-Einstein condensates. These waves can be excited by modulating periodically either the strength of the magnetic trap or the atomic scattering length. To study their dynamics, we develop a variational model that describes consistently both the bulk part of an inhomogeneous, low-density, cigar-shaped condensate and small-amplitude, small-wavelength Faraday waves. The main ansatz used in the variational treatment is tailored around a set of Gaussian envelopes and we show extensions for the high-density regime using a q-Gaussian function. Finally, we show explicitly that for drives of small amplitude, the two methods of obtaining Faraday waves are equivalent, and we discuss the existing experimental results.     

Point-contact study of the heavy-fermion superconductor CeCoIn5

We have investigated the differential conductance spectra of the point contacts between the heavy-fermion superconductor CeCoIn₅ and Pt. Many of them show a double-maximum structure that indicates the superconducting energy gap Δ. The Δ values derived using Blonder-Tinkham-Klapwijk model, however, varies from 0.47 to 0.77 meV, and yet they are within the scatter of the reported values. The evolution of Δ below T_c is slow as compared with that of BCS gap probably reflecting the unconventional superconductivity in CeCoIn₅.     

Magnetic-field induced quantum critical points of valence transition in Ce- and Yb-based heavy fermions

The mechanism of how the magnetic field controls the critical end point of the first-order valence transition is clarified, which is essentially ascribed to charge degrees of freedom. It is shown that the quantum critical point is induced by applying the magnetic field, which explains a peculiar magnetic response in CeIrIn₅ and sharp contrast between X=Ag and Cd for YbXCu₄. Significance of the proximity of the first-order valence transition in the Ce- and Yb-based heavy fermions is pointed out.     

Mean wind: Its velocity and temperature fluctuation in low-Prandtl-number thermal convection

Large-scale circulation in the confined thermal turbulence of mercury is studied experimentally. The instantaneous velocity profile at 128 points is directly measured using ultrasonic velocimetry and the temperature fluctuation is simultaneously obtained by a small thermistor at the cell center. The periodic velocity oscillation is observed for aspect ratios Γ=1,2, but for Γ=0.5. The temperature oscillation is confirmed only in the Γ=2 cell. It is found that the flow patterns depending on the aspect ratio are characterized sufficiently by the joint probability density function up to Ra=4×10⁸.     

Phase transition in dually weighted colored tensor models

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in 1/N of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

Variability of scaling parameters in non-conservative systems: Geophysical aspect

Newly obtained data on the critical dynamics of the drifting/fracturing sea ice in the Arctic Ocean were analyzed and compared with published data on the dynamic processes in the Earth’s crust. Substantial similarities were found in the scaling behavior of both geophysical systems; the most important of them is the b-value space/time variability including a pre-failure drop of this parameter. The b-value pattern of the ensemble of drifting ice floes is an analogue of the b-value distribution over areas and depths in tectonic structures. A common feature of the pre-failure state in the cryosphere and in the Earth’s crust is the increased degree of the energy conservation that manifests itself both in the sea ice consolidation prior to basin-wide ice pack fragmentations, and in involving harder geological formations in the fracture process before earthquakes, respectively. From the viewpoint of the conservative SOC concept, this relation between the system’s conservativity and the occurrence of large-scale fracture events means that the expected scale level of failure is determined by the system’s closeness to “true” SOC behavior.     

Nanoscale observations of the operational failure for phase-change-type nonvolatile memory devices using Ge2Sb2Te5 chalcogenide thin films

In this study, a phase-change memory device was fabricated and the origin of device failure mode was examined using transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS). Ge₂Sb₂Te₅ (GST) was used as the active phase-change material in the memory device and the active pore size was designed to be 0.5 m. After the programming signals of more than 2×10⁶ cycles were repeatedly applied to the device, the high-resistance memory state (reset) could not be rewritten and the cell resistance was fixed at the low-resistance state (set). Based on TEM and EDS studies, Sb excess and Ge deficiency in the device operating region had a strong effect on device reliability, especially under endurance-demanding conditions. An abnormal segregation and oxidation of Ge also was observed in the region between the device operating and inactive peripheral regions. To guarantee an data endurability of more than 1×10¹⁰ cycles of PRAM, it is very important to develop phase-change materials with more stable compositions and to reduce the current required for programming.     

Quantum size effects of Pb overlayers at high coverages

We have studied Pb thin films as a function of the thickness up to 60 monolayers (MLs) using ab initio first principles and model calculations. Magic heights corresponding to a modulated oscillatory pattern of the energy of Pb(1 1 1) films have been measured up to about 30 MLs. We demonstrate that this behaviour continues even for higher thickness due to an extra second modulation pattern in the energetics of the metal film as a function of the number of atomic layers. The origin of this second modulation is the nesting of two close values of the Fermi wavelength in the (1 1 1) direction.