Scalar resonances in a unitary pi pi S-wave model for D(+)->pi(+)pi(-)pi(+)

We propose a model for D(+)->pi(+)pi(-)pi(+) decays following experimental results which indicate that the two-pion interaction in the S wave is dominated by the scalar resonances f(0)(600)/sigma and f(0)(980). The weak decay amplitude for D(+)-> R pi(+), where R is a resonance that subsequently decays into pi(+)pi(-), is constructed in a factorization approach. In the S wave, we implement the strong decay R ->pi(+)pi(-) by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range m(pi pi)(2) from threshold to about 3 GeV(2). In order to reproduce the experimental Dalitz plot for D(+)->pi(+)pi(-)pi(+), we include contributions beyond the S wave. For the P wave, dominated by the rho(770)(0), we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the f(2)(1270) and rho(1450)(0). The major achievement is a good reproduction of the experimental m(pi pi)(2) distribution, and of the partial as well as the total D(+)->pi(+)pi(-)pi(+) branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a by-product, we predict a value for the poorly known D ->sigma transition form factor at q(2)=m pi(2).

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n))

A fully explicit formula for the eigenvalues of Casimir invariants for U-q(gl(m/n)) is given which applies to all unitary irreps. This is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type. These results have applications in the determination of link polynomials arising from unitary irreps of U-q(gl(m/n)).

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

The Early Toarcian anoxia, a synchronous event in the Western Tethys? An approach by quantitative biochronology (Unitary Associations), applied on calcareous nannofossils

During the Early Toarcian, major paleoenvironnemental and paleoceanographical changes occurred, leading to an oceanic anoxic event (OAE) and to a perturbation of the carbon isotope cycle. Although the standard biochronology of the Lower Jurassic is essentially based upon ammonites, in recent years biostratigraphy based on calcareous nannofossils and dinoflagellate cysts is increasingly used to date Jurassic rocks. However, the precise dating and correlation of the Early Toarcian OAE, and of the associated delta C-13 anomaly in different settings of the western Tethys, are still partly problematic, and it is still unclear whether these events are synchronous or not. In order to allow more accurate correlations of the organic rich levels recorded in the Lower Toarcian OAE, this account proposes a new biozonation based on a quantitative biochronology approach, the Unitary Associations (UA), applied to calcareous nannofossils. This study represents the first attempt to apply the UA method to Jurassic nannofossils. The study incorporates eighteen sections distributed across western Tethys and ranging from the Pliensbachian to Aalenian, comprising 1220 samples and 72 calcareous nannofossil taxa. The BioGraph [Savary, J., Guex, J., 1999. Discrete biochronological scales and unitary associations: description of the Biograph Computer program. Memoires de Geologie de Lausanne 34, 282 pp] and UA-Graph (Copyright Hammer O., Guex and Savary, 2002) softwares provide a discrete biochronological framework based upon multi-taxa concurrent range zones in the different sections. The optimized dataset generates nine UAs using the co-occurrences of 56 taxa. These UAs are grouped into six Unitary Association Zones (UA-Z), which constitute a robust biostratigraphic synthesis of all the observed or deduced biostratigraphic relationships between the analysed taxa. The UA zonation proposed here is compared to ``classic'' calcareous nannofossil biozonations, which are commonly used for the southern and the northern sides of Tethys. The biostratigraphic resolution of the UA-Zones varies from one nannofossil subzone or part of it to several subzones, and can be related to the pattern of calcareous nannoplankton originations and extinctions during the studied time interval. The Late Pliensbachian - Early Toarcian interval (corresponding to the UA-Z II) represents a major step in the Jurassic nannoplankton radiation. The recognized UA-Zones are also compared to the carbon isotopic negative excursion and TOC maximum in five sections of central Italy, Germany and England, with the aim of providing a more reliable correlation tool for the Early Toarcian OAE, and of the associated isotopic anomaly, between the southern and northern part of western Tethys. The results of this work show that the TOC maximum and delta C-13 negative excursion correspond to the upper part of the UA-Z II (i.e., UA 3) in the sections analysed. This suggests that the Early Toarcian OAE was a synchronous event within the western Tethys. (c) 2006 Elsevier B.V. All rights reserved.

Chiral unitary approach to eta'N scattering at low energies

We study the eta'N interaction within a chiral unitary approach which includes piN , etaN and related pseudoscalar meson-baryon coupled channels. Since the SU(3) singlet does not contribute to the standard interaction and the eta' is mostly a singlet, the resulting scattering amplitude is very small and inconsistent with experimental estimations of the eta' N scattering length. The additional consideration of vector meson-baryon states into the coupled channel scheme, via normal and anomalous couplings of pseudoscalar to vector mesons, enhances substantially the eta' N amplitude. We also exploit the freedom of adding to the Lagrangian a new term, allowed by the symmetries of QCD, which couples baryons to the singlet meson of SU(3). Adjusting the unknown strength to the eta' N scattering length, we obtain predictions for the elastic eta'N -> etaN and inelastic eta' N -> etaN , piN , KLambda, KEpsilon cross sections at low eta' energies, and discuss their significance.