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.     

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.     

Specific heat of EuIn2P2 at high magnetic fields

We have carried out specific heat measurements on EuIn₂P₂ at high magnetic fields perpendicular to the c-axis in the hexagonal crystal structure in order to understand its thermal properties. The temperature dependence of the specific heat exhibits a clear λ-type anomaly due to a magnetic transition at , indicating that the magnetic transition is of second-order. The λ-type anomaly becomes markedly broader with increasing the magnetic field. This remarkable field-dependence is consistent with the results of previous magnetization measurements which suggest that Eu²⁺ magnetic moments align ferromagnetically perpendicular to the c-axis below T_C. In addition, a hump in the specific heat is observed around 7 K, which can be ascribed to the Zeeman splitting of the Eu²⁺ multiplet by internal magnetic fields.     

Structural modifications of diamond like carbon films induced by MeV nitrogen ion irradiation

Diamond-like carbon (DLC) films were deposited on Si(1 0 0) substrates using plasma deposition technique. The deposited films were irradiated using 2 MeV N⁺ ions at fluences of 1×10¹⁴, 1×10¹⁵ and 5×10¹⁵ ions/cm². Samples have been characterized by using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and high-resolution transmission electron microscopy (HRTEM). Analysis of Raman spectra shows a gradual shift of both D and G band peaks towards higher frequencies along with an increase of the intensity ratio, I(D)/I(G), with increasing ion fluence in irradiation. These results are consistent with an increase of sp² bonding. XPS results also show a monotonic increase of sp²/sp³ hybridization ratio with increasing ion fluence. Plan view TEM images show the formation of clusters in the irradiated DLC films. HRTEM micrographs from the samples irradiated at a fluence of 5×10¹⁵ ions/cm² show the lattice image with an average interplanar spacing of 0.34 nm, revealing that the clusters are graphite clusters. The crystallographic planes in these clusters are somewhat distorted compared to the perfect graphite structure.     

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.     

Large amplitude bending motion in CsOH, studied through ab initio-based three-dimensional potential energy functions

The large-amplitude bending motion in CsOH, a ‘classical’ molecule whose microwave spectrum was first recorded in 1967, has been studied ab initio. The three-dimensional potential energy surface has been calculated at the RCCSD(T)_DK3/[QZP + g ANO-RCC (Cs, O, H)] level of theory and employed in MORBID calculations of the rotation-vibration energies and intensities. The ground electronic state is ¹Σ⁺ with the equilibrium structure r_e(Cs-O) = 2.3930 Å, r_e(O-H) = 0.9587 Å, and ∠_e(Cs-O-H) = 180.0°. The O-H moiety is bound to Cs by an ionic bond and the molecule can be described as Cs^δ+(OH)^δ-. Hence, the bending potential is shallow and gives rise to large-amplitude bending motion. The ro-vibrationally averaged structural parameters, determined as expectation values over MORBID wavefunctions, are 〈r(Cs-O)〉₀ = 2.3987 Å, 〈r(O-H)〉₀ = 0.9754 Å, and 〈∠(Cs-O-H)〉₀ = 163°. Although the averaged structure in the vibrational ground state is far from being linear, the Yamada-Winnewissi-linearity parameter for CsOH is γ₀≈-1.0, the value characteristic for a linear molecule.     

Nuclear matrix elements for rare decays

Neutrinoless double electron capture (0νECEC) is being vigorously investigated because of the possibility of it telling us something about the absolute mass scale of the neutrino. The resonant 0νECEC is particularly interesting due to the potentially huge enhancement of its decay rate by a resonance condition. Recently the mass differences of two atom pairs were measured in order to study the enhancement of the 0νECEC rates of ⁷⁴Se and ¹¹²Sn. The associated nuclear matrix elements were also evaluated. The neutrino mass can also be detected by using beta decays with low Q values. Related to this we have investigated the second-forbidden decay branch of ¹¹⁵In with its ultra-low Q value. Open questions about nuclear and atomic contributions to the associated decay rate emerge.     

Generalised Tsallis statistics in electron-positron collisions

The scaling of charged hadron fragmentation functions to the Tsallis distribution for the momentum fraction 0.01?x?0.2 is presented for various e⁺e⁻ collision energies. A possible microcanonical generalisation of the Tsallis distribution is proposed, which gives good agreement with measured data up to x≈1. The proposal is based on superstatistics and a Koba-Nielsen-Olesen (KNO) like scaling of multiplicity distributions in e⁺e⁻ experiments.     

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.     

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.     

Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors

Muon spin relaxation (μSR) studies of the “1111” and “122” FeAs systems have detected static magnetism with variably sized ordered moments in their parent compounds. The phase diagrams of FeAs, CuO, organic BEDT, A₃C₆₀ and heavy-fermion systems indicate competition between static magnetism and superconductivity, associated with first-order phase transitions at quantum phase boundaries. In both FeAs and CuO systems, the superfluid density n_s/m^* at T→0 exhibits a nearly linear scaling with T_c. Analogous to the roton-minimum energy scaling with the lambda transition temperature in superfluid ⁴He, clear scaling with T_c was also found for the energy of the magnetic resonance mode in cuprates, (Ba,K)Fe₂As₂, CeCoIn₅ and CeCu₂Si₂, as well as the energy of the superconducting coherence peak observed by angle resolved photo emission (ARPES) in the cuprates near (π,0). Both the superfluid density and the energy of these pair-non-breaking soft-mode excitations determine the superconducting T_c via phase fluctuations of condensed bosons. Combining these observations and common dispersion relations of spin and charge collective excitations in the cuprates, we propose a resonant spin-charge motion/coupling, “traffic-light resonance,” expected when the charge energy scale ε_F becomes comparable to the spin fluctuation energy scale ?ω_SF~J, as the process which leads to pair formation in these correlated electron superconductors.     

Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts models in selected spatial structures

Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts (3-state) models is analysed in selected spatial structures. The states are treated as graph nodes, connected by one-spin-flip transitions. The spatial structures are the triangular lattice, the Archimedean (3,¹²²) lattice and the cubic Laves C15 lattice with the periodic boundary conditions. In most cases the ground states are isolated nodes, but for selected systems we obtain connected graphs. The latter means that the magnetisation can vary in time with zero energy cost. The ground states are classified according to their degree and type of neighbours.     

The active role played by nonmagnetic Sr in magnetostructural coupling in SrTcO3 from first principles

The total energies and structural parameters of SrTcO₃ are calculated by means of the generalized gradient approximation (GGA) plus on-site Coulomb interaction corrections (GGA+U) method. G-type antiferromagnetic (G-AFM) is found to be ground state, in consistence with the previous experimental result. The distortions around Sr and Tc upon magnetic transition are compared and the change of distortion for SrO bond upon magnetic transition is found to be 25.83 times of the change for TcO bond. Our results point to an active role played by Sr in magnetostructural coupling in SrTcO₃.     

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.     

Matrix elements of doubly degenerate vibrations and the Herzberg-Teller series

The non-zero terms in doubly degenerate vibrations in the Herzberg-Teller series are discussed and simplified formulae for the matrix elements for transitions between the degenerate l-components of such vibrational levels in upper and lower electronic states are given, with the emphasis on the change of vibrational frequency accompanying the transition. The results are applied to the analysis of degenerate components in the ν₆ and ν₁₆ vibrational transitions in the benzene system, and it is shown that in cases where the second order Herzberg-Teller terms are important, cancelation effects in the matrix elements can lead to the disappearance of certain transitions which are otherwise allowed.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

Tsallis’ statistics in the variability of El Niño/Southern Oscillation during the Holocene epoch

Analysis of the Tsallis q-triplet for the variability of El Niño Southern Oscillation (ENSO) index during the Holocene epoch (last 11,000 years) is presented. Three periods are analyzed, 0-7000, 7000-9700, 9700-11,000 years before the present. During the first and the third periods, the q-index values have the expected usual relations between them (q_sens<1<q_stat<q_rel), and in the second one there is an inversion between q_stat and q_rel (q_stat>q_rel).     

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.