Asymptotic behaviour of zeros of bieberbach polynomials

AbstractLet Ω be a simply-connected domain in the complex plane and let πn denote the nth-degree Bieberbach polynomial approximation to the conformal map f of Ω onto a disc. In this paper we investigate the asymptotic behaviour (as n→σ) of the zeros of πn, πn′ and also of the zeroes of certain closely related rational approximants to f. Our result show that, in each case, the distribution of the zeros is governed by the location of the singularities of the mapping function f in C⧹ω, and we present numerical examples illustrating this

Lyapunov Spectra in SU(2) Lattice Gauge Theory

We develop a method for calculating the Lyapunov characteristic exponents of lattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is obtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with lattice size is found.Comment: 7pp, DUKE-TH-93-5

Setting Children Free: Children’s Independent Movement in the Local Environment

Parental concerns about children’s safety and security are restricting children’s independent exploration of the local environment. Children are being denied important opportunities to exercise, to acquire decision-making skills, such as crossing the road safely, and to develop social skills through interaction with their peers. This paper presents findings from the project CAPABLE (Children’s Activities, Perceptions And Behaviour in the Local Environment) being carried out at University College London. Based on findings from fieldwork carried out with children aged 8-11 in Cheshunt, Hertfordshire, the paper shows the effect of factors such as the number of adults at home, having an older sibling, having a car or garden at home and living near to a park on the propensity to be allowed out alone. Then it considers how being allowed out alone affects the amount of time children spend outdoors, playing with friends and watching television. The paper then uses data from children who have been fitted with physical activity monitors and GPS (Global Positioning Satellite) monitors and asked to keep diaries, to show how children’s travel behaviour differs when they are with adults from when they are not

Learning the Roots of Visual Domain Shift

In this paper we focus on the spatial nature of visual domain shift, attempting to learn where domain adaptation originates in each given image of the source and target set. We borrow concepts and techniques from the CNN visualization literature, and learn domainnes maps able to localize the degree of domain specificity in images. We derive from these maps features related to different domainnes levels, and we show that by considering them as a preprocessing step for a domain adaptation algorithm, the final classification performance is strongly improved. Combined with the whole image representation, these features provide state of the art results on the Office dataset.Comment: Extended Abstrac

Coherent Manipulation of Quantum Delta-kicked Dynamics: Faster-than-classical Anomalous Diffusion

Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system parameters and over long time scales, is shown to display energy absorption that is significantly faster than that associated with the underlying classical anomalous diffusion. The results are of interest to both areas of quantum chaos and quantum control.Comment: 6 pages, 4 figures, to appear in Physical Review

Control of Dynamical Localization

Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of the dynamical localization length, the introduction of classical anomalous diffusion assisted control for systems far from the semiclassical regime, and the observation of a variety of strongly nonexponential lineshapes for dynamical localization. The results provide excellent examples of controlled quantum dynamics in a system that is classically chaotic and offer new opportunities to explore quantum fluctuations and correlations in quantum chaos.Comment: 9 pages, 7 figures, to appear in Physical Review

Phase Control of Nonadiabaticity-induced Quantum Chaos in An Optical Lattice

The qualitative nature (i.e. integrable vs. chaotic) of the translational dynamics of a three-level atom in an optical lattice is shown to be controllable by varying the relative laser phase of two standing wave lasers. Control is explained in terms of the nonadiabatic transition between optical potentials and the corresponding regular to chaotic transition in mixed classical-quantum dynamics. The results are of interest to both areas of coherent control and quantum chaos.Comment: 3 figures, 4 pages, to appear in Physical Review Letter

eta_c production at the Large Hadron Collider

We have studied the production of the 1S_0 charmonium state, eta_c, at the Large Hadron Collider (LHC) in the framework of Non-Relativistic Quantum Chromodynamics (NRQCD) using heavy-quark symmetry. We find that NRQCD predicts a large production cross-section for this resonance at the LHC even after taking account the small branching ratio of eta_c into two photons. We show that it will be possible to test NRQCD through its predictions for eta_c, with the statistics that will be achieved at the early stage of the LHC, running at a center of mass energy of 7 TeV with an integrated luminosity of 100 pb^{-1}Comment: 8 pages, 2 figure