Exact and Scaling Form of the Bipartite Fidelity of the Infinite XXZ Chain

We find an exact expression for the bipartite fidelity f=|'|^2, where |vac> is the vacuum eigenstate of an infinite-size antiferromagnetic XXZ chain and |vac>' is the vacuum eigenstate of an infinite-size XXZ chain which is split in two. We consider the quantity -ln(f) which has been put forward as a measure of quantum entanglement, and show that the large correlation length xi behaviour is consistent with a general conjecture -ln(f) ~ c/8 ln(xi), where c is the central charge of the UV conformal field theory (with c=1 for the XXZ chain). This behaviour is a natural extension of the existing conformal field theory prediction of -ln(f) ~ c/8 ln(L) for a length L bipartite system with 0<< L <<xi.Comment: 6 page

The Peculiar Multi-Wavelength Evolution Of V1535 Sco

We present multi-wavelength observations of the unusual nova V1535 Sco throughout its outburst in 2015. Early radio observations were consistent with synchrotron emission, and early X-ray observations revealed the presence of high-energy (>1 keV) photons. These indicated that strong shocks were present during the first ~2 weeks of the nova's evolution. The radio spectral energy distribution was consistent with thermal emission from week 2 to week 6. Starting in week 7, the radio emission again showed evidence of synchrotron emission and there was an increase in X-ray emission, indicating a second shock event. The optical spectra show evidence for at least two separate outflows, with the faster outflow possibly having a bipolar morphology. The optical and near infrared light curves and the X-ray measurements of the hydrogen column density indicated that the companion star is likely a K giant.Comment: 20 pages, 13 figures, under review at ApJ, updated to match the most recent version submitted to the refere

Bi-partite entanglement entropy in integrable models with backscattering

In this paper we generalise the main result of a recent work by J. L. Cardy and the present authors concerning the bi-partite entanglement entropy between a connected region and its complement. There the expression of the leading order correction to saturation in the large distance regime was obtained for integrable quantum field theories possessing diagonal scattering matrices. It was observed to depend only on the mass spectrum of the model and not on the specific structure of the diagonal scattering matrix. Here we extend that result to integrable models with backscattering (i.e. with non-diagonal scattering matrices). We use again the replica method, which connects the entanglement entropy to partition functions on Riemann surfaces with two branch points. Our main conclusion is that the mentioned infrared correction takes exactly the same form for theories with and without backscattering. In order to give further support to this result, we provide a detailed analysis in the sine-Gordon model in the coupling regime in which no bound states (breathers) occur. As a consequence, we obtain the leading correction to the sine-Gordon partition function on a Riemann surface in the large distance regime. Observations are made concerning the limit of large number of sheets.Comment: 22 pages, 2 figure

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\it J. Phys. A: Math. Gen.} \textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\it Commun. Math. Phys.}, \textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.Comment: 24 pages; minor typos are correcte

Building capacity for co-operative governance as a basis for integrated water resource managing in the Inkomati and Mvoti catchments, South Africa

South Africa’s National Water Act and National Water Resource Strategy set out an ambitious vision for Integrated Water Resources Management including a strong focus on the redistribution of water resources towards the poor and on empowering historically disadvantaged communities. To achieve this vision the Department of Water Affairs &amp; Forestry (DWAF) has been pursuing a programme for devolving powers to 19 stakeholder-led catchment management agencies (CMAs) and more locally, transforming irrigation boards into more inclusive water user associations (WUAs), as well as creating new associations.Co-operative governance is a core principle of this programme. As well as being enshrined in South Africa’s constitution, this principle is seen as key to enabling CMAs to implement their core functions, which include co-ordinating the activities of water users and water management institutions within their water management area. For WUAs also, the principle of co-operative governance is key to building engagement between White commercial farmers and emerging Black farmers, as well as (in some cases) engaging with a wider set of stakeholder interests including local government and environmental interests.Despite a commitment to the principle of co-operative governance, individual and institutional capacity for facilitating co-operative development processes is in relatively short supply within the South African water sector. This paper describes work-in-progress to build capacity in this area, working with:• DWAF’s national Institutional Governance team• The Inkomati CMA (ICMA), the first of South Africa’s new catchment management agencies• Two irrigation boards and a number of other stakeholders in the Mvoti catchment – with a view to the development of an appropriate institutional arrangement (WUA or otherwise) for the co-operative governance of this catchment.This paper focuses on the development of an interactive approach to capacity building in each of these three sites, drawing from a broad portfolio of approaches variously described as social learning, social appraisal, or whole system development. In the Inkomati we have worked primarily with the whole system approach known as Future Search, whereas in the Mvoti we have used the U-process and social appraisal as guiding metaphors and design principles.This paper describes some of our achievements, challenges and reflections to date, and argues that the interactive approaches we have been taking are better suited to the implementation of DWAF’s institutional reform processes than the more established, top-down approaches, which involve issuing guidance, supported by training programmes. The paper concludes with a discussion of the implications for scaling up these types of approaches across the South African water system as a whole, and for the practice of integrated water resource management.Keywords: adaptive IWRM, catchment management agencies, cooperative governance, dialogue, interactive capacity building, social learning, water user association

The Radio Light Curve of the Gamma-Ray Nova in V407 Cyg: Thermal Emission from the Ionized Symbiotic Envelope, Devoured from Within by the Nova Blast

We present multi-frequency radio observations of the 2010 nova event in the symbiotic binary V407 Cygni, obtained with the Karl G. Jansky Very Large Array and spanning 1-45 GHz and 17-770 days following discovery. This nova---the first ever detected in gamma rays---shows a radio light curve dominated by the wind of the Mira giant companion, rather than the nova ejecta themselves. The radio luminosity grew as the wind became increasingly ionized by the nova outburst, and faded as the wind was violently heated from within by the nova shock. This study marks the first time that this physical mechanism has been shown to dominate the radio light curve of an astrophysical transient. We do not observe a thermal signature from the nova ejecta or synchrotron emission from the shock, due to the fact that these components were hidden behind the absorbing screen of the Mira wind. We estimate a mass loss rate for the Mira wind of Mdot_w ~ 10^-6 M_sun/yr. We also present the only radio detection of V407 Cyg before the 2010 nova, gleaned from unpublished 1993 archival VLA data, which shows that the radio luminosity of the Mira wind varies by a factor of >~20 even in quiescence. Although V407 Cyg likely hosts a massive accreting white dwarf, making it a candidate progenitor system for a Type Ia supernova, the dense and radially continuous circumbinary material surrounding V407 Cyg is inconsistent with observational constraints on the environments of most Type Ia supernovae.Comment: Resubmitted to ApJ after incorporating referee's comment

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Radio studies of novae: a current status report and highlights of new results

Novae, which are the sudden visual brightening triggered by runaway thermonuclear burning on the surface of an accreting white dwarf, are fairly common and bright events. Despite their astronomical significance as nearby laboratories for the study of nuclear burning and accretion phenomena, many aspects of these common stellar explosions are observationally not well-constrained and remain poorly understood. Radio observations, modeling and interpretation can potentially play a crucial role in addressing some of these puzzling issues. In this review on radio studies of novae, we focus on the possibility of testing and improving the nova models with radio observations, and present a current status report on the progress in both the observational front and theoretical developments. We specifically address the issues of accurate estimation of ejecta mass, multi-phase and complex ejection phenomena, and the effect of a dense environment around novae. With highlights of new observational results, we illustrate how radio observations can shed light on some of these long-standing puzzles.Comment: 19 pages, 4 figures. Review article published in the Bulletin of the Astronomical Society of India (BASI) special issue on nova

Activity profile of top-class association football referees in relation to fitness test performance and match standard

The aim of this study was to examine the kinematic activity profiles, cardiovascular responses and physical fitness of top-class football referees (n=11) during the FIFA Confederations Cup 2005. Computerised match-analyses (n=9) were performed with a two-dimensional photogrammetric video system, and the cardiovascular demand imposed on the referees (n=12) was measured using heart rate recordings. Total distance covered was 10,218, s=643 m of which 3531, s=510 m was covered at high intensities (>3.6 m.s(-1)). Both total distance covered (r2=0.59; P=0.02) and high-intensity activities (r2=0.44; P=0.05) were related to the distance covered by the ball in the same match. The referees ran at high speed 37% further (P=0.01) in the actual tournament than during under-17 top-level officiating. After the 5-min interval during which high-speed running peaked, in the following 5 min the performance was reduced by 19% (P=0.01) in relation to the mean of the game. Mean heart rate was 161, s=9 b.min(-1) (86, s=3% of maximal heart rate (HRmax)). Mean heart rate (expressed as percentage of HRmax) was related in part (r2=0.36; P5 m.s(-1)) best describes the physical performance of referees; (3) heart rate recording can be a useful tool to determine the most intense periods of a match and (4) the new fitness tests adopted by FIFA were poor predictors of match activities