Physical Sciences and Mathematics Commons^™

Singular Vertices And The Triangulation Space Of The D-Sphere, Simon Catterall, G. Thorleifsson, John B. Kogut, R. Renken

Physics - All Scholarship

By a sequence of numerical experiments we demonstrate that generic triangulations of the D-sphere for D>3 contain one {\it singular} (D-3)-simplex. The mean number of elementary D-simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this (D-3)-simplex also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.

Simple Description Of Pion-Pion Scattering To 1 Gev, Joseph Schechter, Masayasu Harada, Francesco Sannino

Physics - All Scholarship

Motivated by the 1/Nc expansion, we present a simple model of pion-pion scattering as a sum of a `current-algebra' contact term and resonant pole exchanges. The model preserves crossing symmetry as well as unitarity up to 1.2 GeV. Key features include chiral dynamics, vector meson dominance, a broad low energy scalar (sigma) meson and a `Ramsauer-Townsend' mechanism for the understanding of the 980 MeV region. We discuss in detail the `regularization' (corresponding to rescattering effects) necessary to make all these nice features work.

Light-Heavy Symmetry: Geometric Mass Hierarchy For Three Families, Aharon Davidson, Tomer Schwartz, Kameshwar C. Wali

Physics - All Scholarship

The Universal Seesaw pattern coupled with a Light

↔ Heavy symmetry principle leads to the Diophantine equation N =NXi =1ni, where ni ≥ 0 and distinct. Its unique non-trivial solution (3 = 0+1+2) gives rise to the geometric mass hierarchy mW, mWǫ, mWǫ2 for N = 3 fermion families. This is realized in a model where the hybrid (yet Up ↔ Down symmetric) quark mass relations m dmt ≈ m2 c ↔ mumb ≈ m2 s play a crucial role in expressing the CKM mixings in terms of simple mass ratios, notably sin θC ≈ m c m b . …

Peak Effect In Twinned Superconductors, A. I. Larkin, M. Cristina Marchetti, V. M. Vinokur

Physics - All Scholarship

A sharp maximum in the critical current J_c as a function of temperature just below the melting point of the Abrikosov flux lattice has recently been observed in both low and high temperature superconductors. This peak effect is strongest in twinned crystals for fields aligned with the twin planes. We propose that this peak signals the breakdown of the collective pinning regime and the crossover to strong pinning of single vortices on the twin boundaries. This crossover is very sharp and can account for the steep drop of the differential resistivity observed in experiments.

Lattice Quantum Gravity: Review And Recent Developments, Simon Catterall

Physics - All Scholarship

We review the status of different approaches to lattice quantum gravity indicating the successes and problems of each. Recent developments within the dynamical triangulation formulation are then described. Plenary talk at LATTICE 95 July 11-15, Melbourne, Australia.

A Real-Space Renormalization Group For Random Surfaces, Simon Catterall, G. Thorleifsson

Physics - All Scholarship

We propose a new real-space renormalization group transformation for dynamical triangulations. It is shown to preserve geometrical exponents such as the string susceptibility and Hausdorff dimension. We furthermore show evidence for a fixed point structure both in pure gravity and gravity coupled to a critical Ising system. In the latter case we are able to extract estimates for the gravitationally dressed exponents which agree to within 2-3% of the KPZ formula.

The Phase Diagram Of Crystalline Surfaces, Simon Catterall, Konstantinos N. Anagnostopoulos, Mark Bowick, Marco Falcioni, G. Thorleifsson

Physics - All Scholarship

We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to 128^2 nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.

Numerical Results For The Ground-State Interface In A Random Medium, Alan Middleton

Physics - All Scholarship

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These …

Effects Of Symmetry Breaking On The Strong And Electroweak Interactions Of The Vector Nonet, Joseph Schechter, Masayasu Harada

Physics - All Scholarship

Starting from a chiral invariant and quark line rule conserving Lagrangian of pseudoscalar and vector nonets we introduce first and second order symmetry breaking as well as quark line rule violating terms and fit the parameters, at tree level, to many strong and electroweak processes. A number of predictions are made. The electroweak interactions are included in a manifestly gauge invariant manner. The resulting symmetry breaking pattern is discussed in detail. Specifically, for the ``strong'' interactions, we study all the vector meson masses and V -> \phi \phi decays, including isotopic spin violations. In the electroweak sector we study the …

Molecular Hydrogen Formation On Astrophysically Relevant Surfaces, Gianfranco Vidali, N. Katz, Itay Furman, Ofer Biham, Valerio Pirronello

Physics - All Scholarship

Recent experimental results about the formation of molecular hydrogen on astrophysically relevant surfaces under conditions close to those encountered in the interstellar medium are analyzed using rate equations. The parameters of the rate equation model are fitted to temperature-programmed desorption curves obtained in the laboratory. These parameters are the activation energy barriers for atomic hydrogen diffusion and desorption, the barrier for molecular hydrogen desorption, and the probability of spontaneous desorption of a hydrogen molecule upon recombination. The model is a generalization of the Polanyi-Wigner equation and provides a description of both first and second order kinetic processes within a single …

Scaling And The Fractal Geometry Of Two-Dimensional Quantum Gravity, Simon Catterall, G. Thorleifsson, Mark Bowick, V. John

Physics - All Scholarship

We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d_H approx. 3.8, in support of recent theoretical calculations that d_H = 4. We also discuss the back-reaction of matter on the geometry.

Heavy Quark Solitons: Towards Realistic Masses, Joseph Schechter, A. Subbaraman, S. Vaidya, H. Weigel

Physics - All Scholarship

A generalization of the effective meson Lagrangian possessing the heavy quark symmetry to finite meson masses is employed to study the meson mass dependence of the spectrum of S-- and P wave baryons containing one heavy quark or anti-quark. These baryons are described as respectively heavy mesons or anti-mesons bound in the background of a soliton, which is constructed from light mesons. No further approximation is made to solve the bound state equation. For special cases it is shown that the boundary conditions, which have to be satisfied by the bound state wave--functions and stem from the interaction with the …

Resolving Ordering Ambiguities In The Collective Quantization By Particle Conjugation Constraints, Joseph Schechter, H. Weigel

Physics - All Scholarship

We formulate the particle conjugation operation and its convenient realization as G--parity in the framework of several chiral soliton models. The Skyrme model, the Skyrme model with vector mesons and the chiral quark model are specifically treated. The vector and axial vector currents are classified according to their behavior under G--parity. In the soliton sector particle conjugation constrains {\it a priori} ambiguous orderings of operators in the space of the collective coordinates. In the Skyrme model with vector mesons and in a local chiral model with an explicit valence quark this classification scheme provides consistency conditions for the ordering of …

Regge Calculus As A Fourth Order Method In Numerical Relativity, Mark A. Miller

Physics - All Scholarship

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show …

Monte Carlo Studies Of A Novel Lif Radiator For Rich Detectors, Raymond Mountain, A. Efimov, Marina Artuso, Min Gao

Physics - All Scholarship

We show that a multifaceted LiF radiator produces more Cherenkov light and has better resolution per photon than a flat radiator slab when used in a ring imaging Cherenkov counter. Such a system is being considered for the CLEO III upgrade.

Exploring \Pp Scattering In The \1n Picture, Joseph Schechter, Francesco Sannino

Physics - All Scholarship

In the large N_c approximation to QCD, the leading \pp scattering amplitude is expressed as the sum of an infinite number of tree diagrams. We investigate the possibility that an adequate approximation at energies up to somewhat more than one GeV can be made by keeping diagrams which involve the exchange of resonances in this energy range in addition to the simplest chiral contact terms. In this approach crossing symmetry is automatic but individual terms tend to drastically violate partial wave unitarity. We first note that the introduction of the \rho meson in a chirally invariant manner substantially delays the …

Numerical Results For The Ground-State Interface In A Random Medium, Alan Middleton

Physics - All Scholarship

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These …

B_S Mixing Via Ψ K*, Patricia Mcbride, Sheldon Stone

Physics - All Scholarship

The decay mode Bs à ψ K*is suggested as a very good way to measure the Bs mixing parameter xs. These decays can be gathered using a ψ → ℓ+ℓ− trigger. This final state has a well resolved four track decay vertex, useful for good time resolution and background rejection.